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Journal articles on the topic 'Integrodifferentail Equations'

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Published: 5 October 2024

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1

Jargess Abdul Wahid Abdulla, Et al. "Stability Analysis of First Order Integro-Differential Equations With the Successive Approximation Method." Advances in Nonlinear Variational Inequalities 26, no. 2 (July 1, 2023): 46–53. http://dx.doi.org/10.52783/anvi.v26.i2.262.

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The Ulam stability theory provides a framework to provide the stability of functional equations, including integrodifferential equations. This manuscript focuses on the Ulam-stability analysis of the first-order integrodifferential equation. First-order integrodifferential equations combine differential and integral terms, making their analysis challenging and intriguing. The Ulam-stability concept investigates the behaviour of solutions under perturbations in the equation's inputs or initial conditions. It offers valuable insights into the long-term behaviour and robustness of the solutions in the presence of minor disturbances. The results obtained in this study contribute to the understanding of stability properties of first-order integrodifferential equations and provide a foundation for further research in this area. The Ulam stability analysis offers valuable insights into the behaviour of these equations, aiding in their application to diverse domains, including physics, engineering, and mathematical modeling.

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2

Fitzgibbon, William E. "Asymptotic stability for a class of integrodifferential equations." Czechoslovak Mathematical Journal 38, no. 4 (1988): 618–22. http://dx.doi.org/10.21136/cmj.1988.102258.

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3

Bahuguna, D., and L. E. Garey. "Uniqueness of solutions to integrodifferential and functional integrodifferential equations." Journal of Applied Mathematics and Stochastic Analysis 12, no. 3 (January 1, 1999): 253–60. http://dx.doi.org/10.1155/s1048953399000234.

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In this paper we study a class of integrodifferential and functional integro-differential equations with infinite delay. These problems are reformulated as abstract integrodifferential and functional integrodifferential equations. We use Nagumo type conditions to establish the uniqueness of solutions to these abstract equations.

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4

Kiventidis, Thomas. "Positive solutions of integrodifferential and difference equations with unbounded delay." Glasgow Mathematical Journal 35, no. 1 (January 1993): 105–13. http://dx.doi.org/10.1017/s0017089500009629.

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AbstractWe establish a necessary and sufficient condition for the existence of a positive solution of the integrodifferential equationwhere nis an increasing real-valued function on the interval [0, α); that is, if and only if the characteristic equationadmits a positive root.Consider the difference equation , where is a sequence of non-negative numbers. We prove this has positive solution if and only if the characteristic equation admits a root in (0, 1). For general results on integrodifferential equations we refer to the book by Burton [1] and the survey article by Corduneanu and Lakshmikantham [2]. Existence of a positive solution and oscillations in integrodifferential equations or in systems of integrodifferential equations recently have been investigated by Ladas, Philos and Sficas [5], Györi and Ladas [4], Philos and Sficas [12], Philos [9], [10], [11].Recently, there has been some interest in the existence or the non-existence of positive solutions or the oscillation behavior of some difference equations. See Ladas, Philos and Sficas [6], [7].The purpose of this paper is to investigate the positive solutions of integrodifferential equations (Section 1) and difference equations (Section 2) with unbounded delay. We obtain also some results for integrodifferential and difference inequalities.

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5

Bahuguna, D. "Integrodifferential equations with analytic semigroups." Journal of Applied Mathematics and Stochastic Analysis 16, no. 2 (January 1, 2003): 177–89. http://dx.doi.org/10.1155/s1048953303000133.

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In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.

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6

Vlasov, V. V., and N. A. Rautian. "Investigation of Integrodifferential Equations by Methods of Spectral Theory." Contemporary Mathematics. Fundamental Directions 67, no. 2 (December 15, 2021): 255–84. http://dx.doi.org/10.22363/2413-3639-2021-67-2-255-284.

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This paper provides a survey of results devoted to the study of integrodifferential equations with unbounded operator coefficients in a Hilbert space. These equations are operator models of integrodifferential partial differential equations arising in numerous applications: in the theory of viscoelasticity, in the theory of heat propagation in media with memory (Gurtin-Pipkin equations), and averaging theory. The most interesting and profound results of the survey are devoted to the spectral analysis of operator functions that are symbols of the integrodifferential equations under study.

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7

Shabestari, R. Mastani, R. Ezzati, and T. Allahviranloo. "Solving Fuzzy Volterra Integrodifferential Equations of Fractional Order by Bernoulli Wavelet Method." Advances in Fuzzy Systems 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/5603560.

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A matrix method called the Bernoulli wavelet method is presented for numerically solving the fuzzy fractional integrodifferential equations. Using the collocation points, this method transforms the fuzzy fractional integrodifferential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown coefficients. To illustrate the method, it is applied to certain fuzzy fractional integrodifferential equations, and the results are compared.

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8

Wu, Feng. "Sherman-Morrison-Woodbury Formula for Linear Integrodifferential Equations." Mathematical Problems in Engineering 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/9418730.

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The well-known Sherman-Morrison-Woodbury formula is a powerful device for calculating the inverse of a square matrix. The paper finds that the Sherman-Morrison-Woodbury formula can be extended to the linear integrodifferential equation, which results in an unified scheme to decompose the linear integrodifferential equation into sets of differential equations and one integral equation. Two examples are presented to illustrate the Sherman-Morrison-Woodbury formula for the linear integrodifferential equation.

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9

Coville, Jérôme. "Monotonicity in integrodifferential equations." Comptes Rendus Mathematique 337, no. 7 (October 2003): 445–50. http://dx.doi.org/10.1016/j.crma.2003.07.005.

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10

Heard, M. L., and S. M. Rankin. "Nonlinear Volterra Integrodifferential Equations." Journal of Mathematical Analysis and Applications 188, no. 2 (December 1994): 569–89. http://dx.doi.org/10.1006/jmaa.1994.1446.

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11

Qiang, Xiaoli, Kamran, Abid Mahboob, and Yu-Ming Chu. "Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation." Journal of Function Spaces 2020 (December 16, 2020): 1–12. http://dx.doi.org/10.1155/2020/8875792.

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Laplace transform is a powerful tool for solving differential and integrodifferential equations in engineering sciences. The use of Laplace transform for the solution of differential or integrodifferential equations sometimes leads to the solutions in the Laplace domain that cannot be inverted to the real domain by analytic methods. Therefore, we need numerical methods to invert the solution to the real domain. In this work, we construct numerical schemes based on Laplace transform for the solution of fractional-order Volterra integrodifferential equations in the sense of the Atangana-Baleanu Caputo derivative. We propose two numerical methods for approximating the solution of fractional-order linear and nonlinear Volterra integrodifferential equations. In our scheme, the inverse Laplace transform is approximated using a contour integration method and Stehfest method. Some numerical experiments are performed to check the accuracy and efficiency of the methods. The results obtained using these methods are compared.

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12

Kucche, Kishor D., and Pallavi U. Shikhare. "Ulam–Hyers Stability of Integrodifferential Equations in Banach Spaces via Pachpatte’s Inequality." Asian-European Journal of Mathematics 11, no. 04 (August 2018): 1850062. http://dx.doi.org/10.1142/s1793557118500626.

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In this paper, Pachpatte’s inequality is employed to discuss the Ulam–Hyers stabilities for Volterra integrodifferential equations and Volterra delay integrodifferential equations in Banach spaces on both finite and infinite intervals. Examples are given to show the applicability of our obtained results.

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13

Kashkari, Bothayna S. H., and Muhammed I. Syam. "Reproducing Kernel Method for Solving Nonlinear Fractional Fredholm Integrodifferential Equation." Complexity 2018 (December 2, 2018): 1–7. http://dx.doi.org/10.1155/2018/2304858.

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This article is devoted to both theoretical and numerical studies of nonlinear fractional Fredholm integrodifferential equations. In this paper, we implement the reproducing kernel method (RKM) to approximate the solution of nonlinear fractional Fredholm integrodifferential equations. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the solution of the nonlinear fractional Fredholm integrodifferential equation. Uniformly convergence of the approximate solution produced by the RKM to the exact solution is proven.

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14

Grace, Said, and Elvan Akin. "Asymptotic Behavior of Certain Integrodifferential Equations." Discrete Dynamics in Nature and Society 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/4231050.

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This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form:atx′t′=e(t)+∫ct‍(t-s)α-1k(t,s)f(s,x(s))ds, c>1, 0<α<1.From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.

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15

Kamran, Aisha Subhan, Kamal Shah, Suhad Subhi Aiadi, Nabil Mlaiki, and Fahad M. Alotaibi. "Analysis of Volterra Integrodifferential Equations with the Fractal-Fractional Differential Operator." Complexity 2023 (November 9, 2023): 1–22. http://dx.doi.org/10.1155/2023/7210126.

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In this paper, a class of integrodifferential equations with the Caputo fractal-fractional derivative is considered. We study the exact and numerical solutions of the said problem with a fractal-fractional differential operator. The abovementioned operator is arising widely in the mathematical modeling of various physical and biological problems. In our scheme, first, the integrodifferential equation with the fractal-fractional differential operator is converted to an integrodifferential equation with the Riemann–Liouville differential operator. Additionally, the obtained integrodifferential equation is then converted to the equivalent integrodifferential equation involving the Caputo differential operator. Then, we convert the integrodifferential equation under the Caputo differential operator using the Laplace transform to an algebraic equation in the Laplace space. Finally, we convert the obtained solution from the Laplace space into the real domain. Moreover, we utilize two techniques which include analytic inversion and numerical inversion. For numerical inversion of the Laplace transforms, we have to evaluate five methods. Extensive results are presented. Furthermore, for numerical illustration of the abovementioned methods, we consider three problems to demonstrate our results.

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16

Unhale, S. I., and Subhash D. Kendre. "On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order." Journal of Applied Analysis 26, no. 2 (December 1, 2020): 263–72. http://dx.doi.org/10.1515/jaa-2020-2023.

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AbstractThe objective of this work is to study the local existence, uniqueness, stability and other properties of solutions of iterative mixed integrodifferential equations of fractional order. The Successive Approximation Method is applied for the numerical solution of iterative mixed integrodifferential equations of fractional order.

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17

Chen, Yanlai, Tingqiu Cao, and Baoxia Qin. "Multiple Solutions of Boundary Value Problems fornth-Order Singular Nonlinear Integrodifferential Equations in Abstract Spaces." Abstract and Applied Analysis 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/736139.

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The authors discuss multiple solutions for thenth-order singular boundary value problems of nonlinear integrodifferential equations in Banach spaces by means of the fixed point theorem of cone expansion and compression. An example for infinite system of scalar third-order singular nonlinear integrodifferential equations is offered.

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18

Pachpatte, B. "On Approximate Solutions of Certain Mixed Type Integrodifferential Equations." Annals of the Alexandru Ioan Cuza University - Mathematics 57, no. 2 (January 1, 2011): 259–69. http://dx.doi.org/10.2478/v10157-011-0025-0.

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On Approximate Solutions of Certain Mixed Type Integrodifferential Equations The aim of the present paper is to study approximate solutions of mixed Volterra-Fredholm type integrodifferential equations in one and two independent variables. The analysis used in the proofs is based on the applications of new integral inequalities with explicit estimates.

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19

Reinfelds, Andrejs, and Shraddha Christian. "Hyers–Ulam–Rassias Stability of Nonlinear Implicit Higher-Order Volterra Integrodifferential Equations from above on Unbounded Time Scales." Mathematics 12, no. 9 (April 30, 2024): 1379. http://dx.doi.org/10.3390/math12091379.

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In this paper, we present sufficient conditions for Hyers–Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem, and by applying an appropriate Bielecki type norm, the Lipschitz type functions, where Lipschitz coefficient is replaced by unbounded rd-continuous function.

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20

Medveď, Milan. "Two-sided solutions of linear integrodifferential equations of Volterra type with delay." Časopis pro pěstování matematiky 115, no. 3 (1990): 264–72. http://dx.doi.org/10.21136/cpm.1990.118404.

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21

Karakoç, Seydi Battal Gazi, Aytekin Eryılmaz, and Musa Başbük. "The Approximate Solutions of Fredholm Integrodifferential-Difference Equations with Variable Coefficients via Homotopy Analysis Method." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/261645.

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Numerical solutions of linear and nonlinear integrodifferential-difference equations are presented using homotopy analysis method. The aim of the paper is to present an efficient numerical procedure for solving linear and nonlinear integrodifferential-difference equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system.

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22

Baleanu, Dumitru, Sayyedeh Zahra Nazemi, and Shahram Rezapour. "The Existence of Solution for ak-Dimensional System of Multiterm Fractional Integrodifferential Equations with Antiperiodic Boundary Value Problems." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/896871.

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There are many published papers about fractional integrodifferential equations and system of fractional differential equations. The goal of this paper is to show that we can investigate more complicated ones by using an appropriate basic theory. In this way, we prove the existence and uniqueness of solution for ak-dimensional system of multiterm fractional integrodifferential equations with antiperiodic boundary conditions by applying some standard fixed point results. An illustrative example is also presented.

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23

Sezer, Mehmet, and Mustafa Gülsu. "Polynomial approach for the most general linear Fredholm integrodifferential-difference equations using Taylor matrix method." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–15. http://dx.doi.org/10.1155/ijmms/2006/46376.

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A Taylor matrix method is developed to find an approximate solution of the most general linear Fredholm integrodifferential-difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. This method transforms the given general linear Fredholm integrodifferential-difference equations and the mixed conditions to matrix equations with unknown Taylor coefficients. By means of the obtained matrix equations, the Taylor coefficients can be easily computed. Hence, the finite Taylor series approach is obtained. Also, examples are presented and the results are discussed.

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24

Stamov, Gani Tr. "Impulsive Fractional Integrodifferential Equations and Lyapunov Method for Existence of Almost Periodic Solutions." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/861039.

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The plan of this paper is to find conditions for the existence of almost periodic solutions for a class of impulsive fractional integrodifferential equations. The investigations are carried out by using a new fractional comparison principle, coupled with the fractional Lyapunov method. The stability behavior of the almost periodic solutions is also considered, extending the corresponding theory of impulsive integrodifferential equations.

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25

Guo, Dajun. "Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces." Journal of Applied Mathematics and Stochastic Analysis 4, no. 1 (January 1, 1991): 47–69. http://dx.doi.org/10.1155/s1048953391000035.

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In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. As application, we get some results for the third order case. Finally, we give several examples for both infinite and finite systems of ordinary nonlinear integrodifferential equations.

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26

Li, Fang, Jin Liang, Tzon-Tzer Lu, and Huan Zhu. "A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/901942.

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This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach spaceX. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. As an application, the existence of the mild solution to a nonlocal Cauchy problem for a concrete integrodifferential equation is obtained.

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27

Vlasov, V. V., and N. A. Rautian. "Integrodifferential equations in viscoelasticity theory." Russian Mathematics 56, no. 6 (May 24, 2012): 48–51. http://dx.doi.org/10.3103/s1066369x12060060.

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28

Plotnikov, Andrej V., and Tatyana A. Komleva. "Averaging of Set Integrodifferential Equations." Journal Applied Mathematics 1, no. 2 (August 31, 2012): 99–105. http://dx.doi.org/10.5923/j.am.20110102.16.

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29

Słota, Damian, Edyta Hetmaniok, Roman Wituła, Krzysztof Gromysz, and Tomasz Trawiński. "Homotopy Approach for Integrodifferential Equations." Mathematics 7, no. 10 (September 27, 2019): 904. http://dx.doi.org/10.3390/math7100904.

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In this paper, we present the application of the homotopy analysis method for solving integrodifferential equations. In this method, a series is created, the successive elements of which are determined by calculating the appropriate integral of the previous element. In this elaboration, we prove that, if this series is convergent, then its sum is the solution of the objective equation. We formulate and prove the sufficient condition of this convergence, and we give also the estimation of error of an approximate solution obtained by taking the partial sum of the considered series. Moreover, we present in this paper the example of using the investigated method for determining the vibrations of the freely supported reinforced concrete beam as well as for solving the equation of movement of the electromagnet jumper mechanical system.

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30

Vaskevich, V. L., and I. V. Shvab. "Quasilinear integrodifferential Bernoulli-type equations." Journal of Physics: Conference Series 1391 (November 2019): 012075. http://dx.doi.org/10.1088/1742-6596/1391/1/012075.

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31

Lin, Yuhua, and Naoki Tanaka. "Abstract Hyperbolic Volterra Integrodifferential Equations." Journal of Integral Equations and Applications 10, no. 2 (June 1998): 195–218. http://dx.doi.org/10.1216/jiea/1181074221.

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32

Keck, David N., and Mark A. McKibben. "Abstract stochastic integrodifferential delay equations." Journal of Applied Mathematics and Stochastic Analysis 2005, no. 3 (January 1, 2005): 275–305. http://dx.doi.org/10.1155/jamsa.2005.275.

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We investigate a class of abstract stochastic integrodifferential delay equations dependent upon a family of probability measures in a separable Hilbert space. We establish the existence and uniqueness of a mild solution, along with various continuous dependence estimates and Markov (weak and strong) properties of this solution. This is followed by a convergence result concerning the strong solutions of the Yosida approximations of our equation, from which we deduce the weak convergence of the measures induced by these strong solutions to the measure induced by the mild solution of the primary problem under investigation. Next, we establish the pth moment and almost sure exponential stability of the mild solution. Finally, an analysis of two examples, namely a generalized stochastic heat equation and a Sobolev-type evolution equation, is provided to illustrate the applicability of the general theory.

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33

Oka, Hirokazu. "Abstract quasilinear Volterra integrodifferential equations." Nonlinear Analysis: Theory, Methods & Applications 28, no. 6 (March 1997): 1019–45. http://dx.doi.org/10.1016/s0362-546x(97)82858-1.

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34

Coville, Jérome, and Louis Dupaigne. "Travelling fronts in integrodifferential equations." Comptes Rendus Mathematique 337, no. 1 (July 2003): 25–30. http://dx.doi.org/10.1016/s1631-073x(03)00216-4.

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35

Burton, T. A. "Periodic Solutions of Integrodifferential Equations." Journal of the London Mathematical Society s2-31, no. 3 (June 1985): 537–48. http://dx.doi.org/10.1112/jlms/s2-31.3.537.

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36

de Laubenfels, Ralph. "Integrated semigroups and integrodifferential equations." Mathematische Zeitschrift 204, no. 1 (December 1990): 501–14. http://dx.doi.org/10.1007/bf02570889.

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37

Pupyshev, V. V. "On three-particle integrodifferential equations." Theoretical and Mathematical Physics 81, no. 1 (October 1989): 1072–77. http://dx.doi.org/10.1007/bf01015511.

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38

Grimmer, Ronald, and James H. Liu. "Integrated semigroups and integrodifferential equations." Semigroup Forum 48, no. 1 (December 1994): 79–95. http://dx.doi.org/10.1007/bf02573656.

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39

Nagel, Rainer, and Eugenio Sinestrari. "Nonlinear hyperbolic volterra integrodifferential equations." Nonlinear Analysis: Theory, Methods & Applications 27, no. 2 (July 1996): 167–86. http://dx.doi.org/10.1016/0362-546x(95)00018-q.

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40

Philos, Ch G. "Positive solutions of integrodifferential equations." Journal of Applied Mathematics and Stochastic Analysis 6, no. 1 (January 1, 1993): 55–68. http://dx.doi.org/10.1155/s1048953393000061.

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Integrodifferential equations of the forms x′(t)+p(t)∫0tK(t−s)x(s)ds=0 and x′(t)+q(t)∫−∞tK(t−s)x(s)ds=0 are considered, where K∈C([0,∞),[0,∞)), p∈C([0,∞),[0,∞)) and q∈C((−∞,∞),[0,∞)). Necessary conditions and also sufficient conditions for the existence of positive solutions are established.

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41

Shekarabi, F. Hosseini. "Sinc Collocation Method for Finding Numerical Solution of Integrodifferential Model Arisen in Continuous Mixed Strategy." Journal of Computational Engineering 2014 (September 17, 2014): 1–8. http://dx.doi.org/10.1155/2014/320420.

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One of the new techniques is used to solve numerical problems involving integral equations and ordinary differential equations known as Sinc collocation methods. This method has been shown to be an efficient numerical tool for finding solution. The construction mixed strategies evolutionary game can be transformed to an integrodifferential problem. Properties of the sinc procedure are utilized to reduce the computation of this integrodifferential to some algebraic equations. The method is applied to a few test examples to illustrate the accuracy and implementation of the method.

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42

Li, Fang. "Existence of the Mild Solutions for Delay Fractional Integrodifferential Equations with Almost Sectorial Operators." Abstract and Applied Analysis 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/729615.

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This paper is concerned with the existence of mild solutions for the fractional integrodifferential equations with finite delay and almost sectorial operators in a separable Banach spaceX. We obtain existence theorem for mild solutions to the above-mentioned equations, by means of measure of noncompactness and the resolvent operators associated with almost sectorial operators. As an application, the existence of mild solutions for some integrodifferential equation is obtained.

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43

Keck, David N., and Mark A. McKibben. "Abstract semilinear stochastic Itó-Volterra integrodifferential equations." Journal of Applied Mathematics and Stochastic Analysis 2006 (July 4, 2006): 1–22. http://dx.doi.org/10.1155/jamsa/2006/45253.

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We consider a class of abstract semilinear stochastic Volterra integrodifferential equations in a real separable Hilbert space. The global existence and uniqueness of a mild solution, as well as a perturbation result, are established under the so-called Caratheodory growth conditions on the nonlinearities. An approximation result is then established, followed by an analogous result concerning a so-called McKean-Vlasov integrodifferential equation, and then a brief commentary on the extension of the main results to the time-dependent case. The paper ends with a discussion of some concrete examples to illustrate the abstract theory.

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44

Yi, Mingxu, Kangwen Sun, Jun Huang, and Lifeng Wang. "Numerical Solutions of Fractional Integrodifferential Equations of Bratu Type by Using CAS Wavelets." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/801395.

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A numerical method based on the CAS wavelets is presented for the fractional integrodifferential equations of Bratu type. The CAS wavelets operational matrix of fractional order integration is derived. A truncated CAS wavelets series together with this operational matrix is utilized to reduce the fractional integrodifferential equations to a system of algebraic equations. The solution of this system gives the approximation solution for the truncated limited2k(2M+1). The convergence and error estimation of CAS wavelets are also given. Two examples are included to demonstrate the validity and applicability of the approach.

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45

Maayah, Banan, Feras Yousef, Omar Arqub, Shaher Momani, and Ahmed Alsaedi. "Computing bifurcations behavior of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types in hilbert space with error analysis." Filomat 33, no. 12 (2019): 3845–53. http://dx.doi.org/10.2298/fil1912845m.

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In this article, we propose and analyze a computational method for the numerical solutions of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types. The method provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n-term of exact solutions, numerical solutions of linear and nonlinear singular time-fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. The utilized results show that the present method and simulated annealing provide a good scheduling methodology to such singular integrodifferential equations.

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Ryabov, Y. A. "Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect." Mathematica Bohemica 120, no. 3 (1995): 265–82. http://dx.doi.org/10.21136/mb.1995.126010.

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Grimmer, R., and J. H. Liu. "Limiting Equations of Integrodifferential Equations in Banach Space." Journal of Mathematical Analysis and Applications 188, no. 1 (November 1994): 78–91. http://dx.doi.org/10.1006/jmaa.1994.1412.

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Geiser, Jürgen. "Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/812137.

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Abstract:

We present novel iterative splitting methods to solve integrodifferential equations. Such integrodifferential equations are applied, for example, in scattering problems of plasma simulations. We concentrate on a linearised integral part and a reformulation to a system of first order differential equations. Such modifications allow for applying standard iterative splitting schemes and for extending the schemes, respecting the integral operator. A numerical analysis is presented of the system of semidiscretised differential equations as abstract Cauchy problems. In the applications, we present benchmark and initial realistic applications to transport problems with scattering terms. We also discuss the benefits of such iterative schemes as fast solver methods.

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Faris, Hewa Selman, and Raad Noori Butris. "Existence, Uniqueness, and Stability of Solutions of Systems of Complex Integrodifferential Equations on Complex Planes." WSEAS TRANSACTIONS ON MATHEMATICS 21 (March 3, 2022): 90–97. http://dx.doi.org/10.37394/23206.2022.21.14.

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In this paper, we investigate the existence, uniqueness, and stability of solutions for a class of systems of non-linear complex Integrodifferential equations on complex planes. Based on the complex Integrodifferential equations, the iterative sequences for approximating the solutions are derived and several theorems about the existence and the forms of entire solutions are established. Finally, numerical results are illustrated from an example to confirm the veracity and applicability of the main problem whose exact solutions are available.

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Balachandran, K., and J. Y. Park. "Existence of solutions and controllability of nonlinear integrodifferential systems in Banach spaces." Mathematical Problems in Engineering 2003, no. 2 (2003): 65–79. http://dx.doi.org/10.1155/s1024123x03201022.

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Abstract:

We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed-point theorem. Examples are provided to illustrate the theory.

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