Thematische Bibliographien / Caputo's approach

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Auswahl der wissenschaftlichen Literatur zum Thema „Caputo's approach“

Autor: Grafiati

Veröffentlicht am 28. Juni 2021

Zuletzt aktualisiert am 1. Februar 2022

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Zeitschriftenartikel zum Thema "Caputo's approach"

Al-Refai, Mohammed, Mohamed Ali Hajji und Muhammad I. Syam. „An Efficient Series Solution for Fractional Differential Equations“. Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/891837.

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We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of Caputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivatives, which do not compute in general. The terms of the series are determined sequentially with explicit formula, where only integer derivatives have to be computed. The efficiency of the new algorithm is illustrated through several examples. Comparison with other series methods such as the Adomian decomposition method and the homotopy perturbation method is made to indicate the efficiency of the new approach. The algorithm can be implemented for a wide class of fractional differential equations with different types of fractional derivatives.

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Alofi, Abdulaziz, Jinde Cao, Ahmed Elaiw und Abdullah Al-Mazrooei. „Delay-Dependent Stability Criterion of Caputo Fractional Neural Networks with Distributed Delay“. Discrete Dynamics in Nature and Society 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/529358.

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This paper is concerned with the finite-time stability of Caputo fractional neural networks with distributed delay. The factors of such systems including Caputo’s fractional derivative and distributed delay are taken into account synchronously. For the Caputo fractional neural network model, a finite-time stability criterion is established by using the theory of fractional calculus and generalized Gronwall-Bellman inequality approach. Both the proposed criterion and an illustrative example show that the stability performance of Caputo fractional distributed delay neural networks is dependent on the time delay and the order of Caputo’s fractional derivative over a finite time.

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Brouwer, Rein. „“Fragment of What Will Happen”“. Religion and the Arts 23, Nr. 4 (10.10.2019): 384–410. http://dx.doi.org/10.1163/15685292-02304003.

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Abstract The Swedish poet Tomas Tranströmer (1931–2015), winner of the 2011 Nobel Prize in Literature, is known for the perceptive metaphors in his poems “couched in deceptively spare language, crystalline descriptions of natural beauty and explorations of the mysteries of identity and creativity.” Although Tranströmer himself never made a secret of the religious tendency in his work, there is some discussion about the importance of the religious dimension in his poems, which are widely acclaimed in Sweden, a predominately secular country. This article discusses several discourses exploring the religious dimensions of Tranströmer’s poetry, and presents a new approach for understanding the religious and spiritual aspects of his art based on the work of philosopher of religion John D. Caputo. Caputo’s “hauntology” is claimed to be conducive in reading Tranströmer’s poetry as a religious text. A “hauntological” reading of the poetry of Tranströmer interprets the event that is haunting the poems, and suggests a new way of conceiving a religious insight in a work of modern art.

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Taïeb, Amele, und Zoubir Dahmani. „Generalized Isoperimetric FVPs Via Caputo Approach“. Acta Mathematica 56 (2019): 23–40. http://dx.doi.org/10.4467/20843828am.19.003.12111.

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Jean-Claude, Trigeassou, Maamri Nezha und Oustaloup Alain. „The Caputo Derivative And The Infinite State Approach“. IFAC Proceedings Volumes 46, Nr. 1 (Februar 2013): 587–92. http://dx.doi.org/10.3182/20130204-3-fr-4032.00122.

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Koca, Ilknur, und Pelin Yaprakdal. „A new approach for nuclear family model with fractional order Caputo derivative“. Applied Mathematics and Nonlinear Sciences 5, Nr. 1 (31.03.2020): 393–404. http://dx.doi.org/10.2478/amns.2020.1.00037.

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AbstractA work on a mathematical modeling is very popular in applied sciences. Nowadays many mathematical models have been considered and new methods have been used for approaching of these models. In this paper we are considering mathematical modeling of nuclear family model with fractional order Caputo derivative. Also the existence and uniqueness results and numerical scheme are given with Adams-Bashforth scheme via fractional order Caputo derivative.

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Evirgen, Fırat, und Mehmet Yavuz. „An Alternative Approach for Nonlinear Optimization Problem with Caputo - Fabrizio Derivative“. ITM Web of Conferences 22 (2018): 01009. http://dx.doi.org/10.1051/itmconf/20182201009.

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In this study, a fractional mathematical model with steepest descent direction is proposed to find optimal solutions for a class of nonlinear programming problem. In this sense, Caputo-Fabrizio derivative is adapted to the mathematical model. To demonstrate the solution trajectory of the mathematical model, we use the multistage variational iteration method (MVIM). Numerical simulations and comparisons on some test problems show that the mathematical model generated using Caputo-Fabrizio fractional derivative is both feasible and efficient to find optimal solutions for a certain class of equality constrained optimization problems.

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Hasan, Nabaa N., und Zainab John. „Analytic Approach for Solving System of Fractional Differential Equations“. Al-Mustansiriyah Journal of Science 32, Nr. 1 (21.02.2021): 14. http://dx.doi.org/10.23851/mjs.v32i1.929.

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In this paper, Sumudu transformation (ST) of Caputo fractional derivative formulae are derived for linear fractional differential systems. This formula is applied with Mittage-Leffler function for certain homogenous and nonhomogenous fractional differential systems with nonzero initial conditions. Stability is discussed by means of the system's distinctive equation.

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Hoa, Ngo Van, Ho Vu und Tran Minh Duc. „Fuzzy fractional differential equations under Caputo–Katugampola fractional derivative approach“. Fuzzy Sets and Systems 375 (November 2019): 70–99. http://dx.doi.org/10.1016/j.fss.2018.08.001.

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Albadarneh, Ramzi B., Iqbal Batiha, A. K. Alomari und Nedal Tahat. „Numerical approach for approximating the Caputo fractional-order derivative operator“. AIMS Mathematics 6, Nr. 11 (2021): 12743–56. http://dx.doi.org/10.3934/math.2021735.

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<abstract><p>This work aims to propose a new simple robust power series formula with its truncation error to approximate the Caputo fractional-order operator $ D_{a}^{\alpha}y(t) $ of order $ m-1 < \alpha < m $, where $ m\in\mathbb{N} $. The proposed formula, which are derived with the help of the weighted mean value theorem, is expressed ultimately in terms of a fractional-order series and its reminder term. This formula is used successfully to provide approximate solutions of linear and nonlinear fractional-order differential equations in the form of series solution. It can be used to determine the analytic solutions of such equations in some cases. Some illustrative numerical examples, including some linear and nonlinear problems, are provided to validate the established formula.</p></abstract>

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Dissertationen zum Thema "Caputo's approach"

Šustková, Apolena. „Řešení obyčejných diferenciálních rovnic neceločíselného řádu metodou Adomianova rozkladu“. Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445455.

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This master's thesis deals with solving fractional-order ordinary differential equations by the Adomian decomposition method. A part of the work is therefore devoted to the theory of equations containing differential operators of non-integer order, especially the Caputo operator. The next part is devoted to the Adomian decomposition method itself, its properties and implementation in the case of Chen system. The work also deals with bifurcation analysis of this system, both for integer and non-integer case. One of the objectives is to clarify the discrepancy in the literature concerning the fractional-order Chen system, where experiments based on the use of the Adomian decomposition method give different results for certain input parameters compared with numerical methods. The clarification of this discrepancy is based on recent theoretical knowledge in the field of fractional-order differential equations and their systems. The conclusions are supported by numerical experiments, own code implementing the Adomian decomposition method on the Chen system was used.

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Muniswamy, Sowmya. „Analytical and Numerical Approach to Caputo Fractional Differential Equations via Generalized Iterative Schemes with Applications“. Thesis, University of Louisiana at Lafayette, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3622948.

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Natural lower and upper solutions for initial value problems guarantees the interval of existence. However, coupled lower and upper solutions used as initial approximation in generalized iterative method are very useful since the iterates can be computed without any extra assumption. Generalized monotone method, along with the method of lower and upper solutions, has been used to develop the coupled lower and upper solutions on an extended interval for both scalar and system of Caputo fractional differential equations. This method yields linear convergence. Generalized quasilinearization method, along with the method of lower and upper solutions, was used to compute the coupled minimal and maximal solutions, if coupled lower and upper solutions existed for the scalar Caputo fractional differential equations. This method yielded quadratic convergence. Also, a mixed method of monotone method and quasilinearization method was developed to compute the coupled minimal and maximal solutions, if coupled lower and upper solutions existed, for the scalar Caputo fractional differential equations. This mixed method was used to compute the coupled lower and upper solutions on the desired interval, which yielded superlinear convergence. Numerical examples have been provided as an application of the analytical results.

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Hernández-Hernández, Ma Elena. „On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type“. Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/88783/.

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This dissertation focuses on the study of generalized fractional differential equations involving a general class of non-local operators which are referred to as the generalized fractional derivatives of Caputo and Riemann-Liouville (RL) type. These operators were introduced recently as a probabilistic extension of the classical fractional Caputo and Riemann-Liouville derivatives of order β ε (0,1) (when acting on regular enough functions). The main contribution of this work lies in displaying the use of stochastic analysis as a valuable approach for the study of fractional differential equations and their generalizations. The stochastic representations presented here also lead to many interesting potential applications, e.g., by providing new numerical approaches to approximate solutions to equations for which an explicit solution is not available.

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Buchteile zum Thema "Caputo's approach"

Diethelm, Kai. „Caputo’s Approach“. In Lecture Notes in Mathematics, 49–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14574-2_3.

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„Caputi’s Alternative Approach to Clinical Evaluation“. In Teaching in Nursing and Role of the Educator. New York, NY: Springer Publishing Company, 2017. http://dx.doi.org/10.1891/9780826140142.ap03.

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Konferenzberichte zum Thema "Caputo's approach"

Faieghi, Mohammad Reza, Hadi Delavari und Ali Akbar Jalali. „Control of Lorenz system with a novel fractional controller: A Caputo's differintegration based approach“. In 2011 2nd International Conference on Control, Instrumentation, and Automation (ICCIA). IEEE, 2011. http://dx.doi.org/10.1109/icciautom.2011.6356729.

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Pandey, Rajesh K., und Om P. Agrawal. „Numerical Scheme for Generalized Isoparametric Constraint Variational Problems With A-Operator“. In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12388.

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This paper presents a numerical scheme for a class of Isoperimetric Constraint Variational Problems (ICVPs) defined in terms of an A-operator introduced recently. In this scheme, Bernstein’s polynomials are used to approximate the desired function and to reduce the problem from a functional space to an eigenvalue problem in a finite dimensional space. Properties of the eigenvalues and eigenvectors of this problem are used to obtain approximate solutions to the problem. Results for two examples are presented to demonstrate the effectiveness of the proposed scheme. In special cases the A-operator reduce to Riemann-Liouville, Caputo, Riesz-Riemann-Liouville and Riesz-Caputo, and several other fractional derivatives defined in the literature. Thus, the approach presented here provides a general scheme for ICVPs defined using different types of fractional derivatives. Although, only Bernstein’s polynomials are used here to approximate the solutions, many other approximation schemes are possible. Effectiveness of these approximation schemes will be presented in the future.

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Agrawal, Om P. „A Numerical Scheme and an Error Analysis for a Class of Fractional Optimal Control Problems“. In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87367.

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There has been a growing interest in recent years in the area of Fractional Optimal Control (FOC). In this paper, we present a formulation for a class of FOC problems, in which a performance index is defined as an integral of a quadratic function of the state and the control variables, and a dynamic constraint is defined as a Fractional Differential Equation (FDE) linear in both the state and the control variables. The fractional derivative is defined in the Caputo sense. In this formulation, the FOC problem is reduced to a Fractional Variational Problem (FVP), and the necessary differential equations for the problems are obtained using the recently developed theories for FVPs. For the numerical solutions of the problems, a direct approach is taken in which the solutions are approximated using a truncated Fractional Power Series (FPS). An error analysis is also performed. It is demonstrated that the solution converges from above in the sense that the value of the approximate performance index is always higher than the optimum performance index. An expression for the error in the performance index is also given. The application of a FPS and an optimality criterion reduces the FOC to a set of linear algebraic equations which are solved using a linear solver. It is demonstrated numerically that the solution converges as the number of terms in the series increases, and the approximate solution approaches to the analytical solution as the order of the fractional derivative approaches to an integer order derivative. Numerical results are presented to demonstrate the performance of the Formulation.

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Magin, Richard L., und Dumitru Baleanu. „NMR Measurements of Anomalous Diffusion Reflect Fractional Order Dynamics“. In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34224.

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Diffusion weighted MRI is often used to detect and stage neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion measurements relies on the design of selective phase encoding pulses that alter the intensity of the acquired signal according to biophysical models of spin diffusion in tissue. The most common approach utilizes a bipolar or Stejskal-Tanner gradient pulse sequence to encode the apparent diffusion coefficient as an exponential, multi-exponential or stretched exponential function of experimentally-controlled parameters. Several studies have investigated the ability of the stretched exponential to provide an improved fit to diffusion-weighted imaging data. These results were recently analyzed by establishing a direct link between water diffusion, as measured using NMR, and fractal structural models of tissues. In this paper we suggest an alternative description for stretched exponential behavior that reflects fractional order dynamics of a generalized Bloch-Torrey equation in either space or time. Such generalizations are the basis for similar anomalous diffusion phenomena observed in optical spectroscopy, polymer dynamics and electrochemistry. Here we demonstrate a correspondence between the detected NMR signal and anomalous diffusional dynamics of water through the Riesz fractional order space derivative and the Caputo form of the fractional order Riemann-Liouville time derivative.

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Agrawal, Om P., Md Mehedi Hasan und X. W. Tangpong. „A Numerical Scheme for a Class of Parametric Problem of Fractional Variational Calculus“. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48768.

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Fractional derivatives (FDs) or derivatives of arbitrary order have been used in many applications, and it is envisioned that in future they will appear in many functional minimization problems of practical interest. Since fractional derivatives have such property as being non-local, it can be extremely challenging to find analytical solutions for fractional parametric optimization problems, and in many cases, analytical solutions may not exist. Therefore, it is of great importance to develop numerical methods for such problems. This paper presents a numerical scheme for a linear functional minimization problem that involves FD terms. The FD is defined in terms of the Riemann-Liouville definition; however, the scheme will also apply to Caputo derivatives, as well as other definitions of fractional derivatives. In this scheme, the spatial domain is discretized into several subdomains and 2-node one-dimensional linear elements are adopted to approximate the solution and its fractional derivative at point within the domain. The fractional optimization problem is converted to an eigenvalue problem, the solution of which leads to fractional orthogonal functions. Convergence study of the number of elements and error analysis of the results ensure that the algorithm yields stable results. Various fractional orders of derivative are considered and as the order approaches the integer value of 1, the solution recovers the analytical result for the corresponding integer order problem.

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