Dissertations / Theses on the topic 'Fractional derivatives at zero'
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Wang, Zhibo. "Estimations non-asymptotiques et robustes basées sur des fonctions modulatrices pour les systèmes d'ordre fractionnaire." Electronic Thesis or Diss., Bourges, INSA Centre Val de Loire, 2023. http://www.theses.fr/2023ISAB0003.
Full textThis thesis develops the modulating functions method for non-asymptotic and robust estimations for fractional-order nonlinear systems, fractional-order linear systems with accelerations as output, and fractional-order time-delay systems. The designed estimators are provided in terms of algebraic integral formulas, which ensure non-asymptotic convergence. As an essential feature of the designed estimation algorithms, noisy output measurements are only involved in integral terms, which endows the estimators with robustness against corrupting noises. First, for fractional-order nonlinear systems which are partially unknown, fractional derivative estimation of the pseudo-state is addressed via the modulating functions method. Thanks to the additive index law of fractional derivatives, the estimation is decomposed into the fractional derivatives estimation of the output and the fractional initial values estimation. Meanwhile, the unknown part is fitted via an innovative sliding window strategy. Second, for fractional-order linear systems with accelerations as output, fractional integral estimation of the acceleration is firstly considered for fractional-order mechanical vibration systems, where only noisy acceleration measurements are available. Based on the existing numerical approaches addressing the proper fractional integrals of accelerations, our attention is primarily restricted to estimating the unknown initial values using the modulating functions method. On this basis, the result is further generalized to more general fractional-order linear systems. In particular, the behaviour of fractional derivatives at zero is studied for absolutely continuous functions, which is quite different from that of integer order. Third, for fractional-order time-delay systems, pseudo-state estimation is studied by designing a fractional-order auxiliary modulating dynamical system, which provides a more general framework for generating the required modulating functions. With the introduction of the delay operator and the bicausal generalized change of coordinates, the pseudo-state estimation of the considered system can be reduced to that of the corresponding observer normal form. In contrast to the previous work, the presented scheme enables direct estimation for the pseudo-state rather than estimating the fractional derivatives of the output and a bunch of fractional initial values. In addition, the efficiency and robustness of the proposed estimators are verified by numerical simulations in this thesis. Finally, a summary of this work and an insight into future work were drawn
Katugampola, Don Udita Nalin. "ON GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES." OpenSIUC, 2011. https://opensiuc.lib.siu.edu/dissertations/387.
Full textSchiavone, S. E. "Distributional theories for multidimensional fractional integrals and derivatives." Thesis, University of Strathclyde, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382492.
Full textTraytak, Sergey D., and Tatyana V. Traytak. "Method of fractional derivatives in time-dependent diffusion." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-193646.
Full textTraytak, Sergey D., and Tatyana V. Traytak. "Method of fractional derivatives in time-dependent diffusion." Diffusion fundamentals 6 (2007) 38, S. 1-2, 2007. https://ul.qucosa.de/id/qucosa%3A14215.
Full textMunkhammar, Joakim. "Riemann-Liouville Fractional Derivatives and the Taylor-Riemann Series." Thesis, Uppsala University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121418.
Full textHaveroth, Thais Clara da Costa. "On the use of fractional derivatives for modeling nonlinear viscoelasticity." Universidade do Estado de Santa Catarina, 2015. http://tede.udesc.br/handle/handle/2069.
Full textCoordenação de Aperfeiçoamento de Pessoal de Nível Superior
Dentre a vasta gama de polímeros estruturais atualmente disponíveis no mercado, este trabalho está particularmente voltado ao estudo do polietileno de alta densidade. Embora este material já tenha sido investigado por diversos autores, seu típico comportamento viscoelástico não-linear apresenta dificuldades na modelagem. Visando uma nova contribuição, este trabalho propõe a descrição de tal comportamento utilizando uma abordagem baseada em derivadas fracionários. Esta formulação produz equações constitutivas fracionais que resultam em boas propriedades de ajuste de curvas com menos parâmetros a serem identificados que nos métodos tradicionais. Neste sentido, os resultados experimentais de fluência para o polietileno de alta densidade, avaliados em diferentes níveis de tensão, são ajustados por este esquema. Para estimar a deformação à níveis de tensão que não tenham sido medidos experimentalmente, o princípio da equivalência tensão-tempo é utilizado e os resultados são comparados com aqueles apresentados por uma interpolação linear dos parâmetros. Além disso, o princípio da superposição modificado é aplicado para predizer a comportamento de materiais sujeitos a níveis de tensão que mudam abruptamente ao longo do tempo. Embora a abordagem fracionária simplifique o problema de otimização inversa subjacente, é observado um grande aumento no esforço computacional. Assim, alguns algoritmos que objetivam economia computacional, são estudados. Conclui-se que, quando acurária é necessária ou quando um modelo de séries Prony requer um número muito grande de parâmetros, a abordagem fracionária pode ser uma opção interessante.
Among the wide range of structural polymers currently available in the market, this work is concerned particularly with high density polyethylene. The typical nonlinear viscoelastic behavior presented by this material is not trivial to model, and has already been investigated by many authors in the past. Aiming at a further contribution, this work proposes modeling this material behavior using an approach based on fractional derivatives. This formulation produces fractional constitutive equations that result in good curve-fitting properties with less parameters to be identified when compared to traditional methods. In this regard, experimental creep results of high density polyethylene evaluated at different stress levels are fitted by this scheme. To estimate creep at stress levels that have not been measured experimentally, the time-stress equivalence principle is used and the results are compared with those presented by a linear interpolation of the parameters. Furthermore, the modified superposition principle is applied to predict the strain for materials subject to stress levels which change abruptly from time to time. Some comparative results are presented showing that the fractional approach proposed in this work leads to better results in relation to traditional formulations described in the literature. Although the fractional approach simplifies the underlying inverse optimization problem, a major increase in computational effort is observed. Hence, some algorithms that show computational cost reduction, are studied. It is concluded that when high accuracy is mandatory or when a Prony series model requires a very large number of parameters, the fractional approach may be an interesting option.
Shi, Chen Yang. "High order compact schemes for fractional differential equations with mixed derivatives." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691348.
Full textAtkins, Zoe. "Almost sharp fronts : limit equations for a two-dimensional model with fractional derivatives." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/55759/.
Full textJarrah, Bilal. "Fractional Order and Inverse Problem Solutions for Plate Temperature Control." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40551.
Full textBlanc, Emilie. "Time-domain numerical modeling of poroelastic waves : the Biot-JKD model with fractional derivatives." Phd thesis, Aix-Marseille Université, 2013. http://tel.archives-ouvertes.fr/tel-00954506.
Full textShabankhah, Mahmood. "Integral means of the derivatives of Blaschke products and zero sequences for the Dirichlet space." Thesis, Université Laval, 2008. http://www.theses.ulaval.ca/2008/25900/25900.pdf.
Full textFernandez, Arran. "Analysis in fractional calculus and asymptotics related to zeta functions." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/284390.
Full textJiang, Xin. "A Systematic Approach for Digital Hardware Realization of Fractional-Order Operators and Systems." University of Akron / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=akron1386649994.
Full textMucha, Ján. "Pokročilé metody parametrizace online písma osob s grafomotorickými obtížemi." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2021. http://www.nusl.cz/ntk/nusl-438731.
Full textTeodoro, Graziane Sales 1990. "Cálculo fracionário e as funções de Mittag-Leffler." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306995.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: O cálculo fracionário, nomenclatura utilizada para cálculo de ordem não inteira, tem se mostrado importante e, em muitos casos, imprescindível na discussão de problemas advindos de diversas áreas da ciência, como na matemática, física, engenharia, economia e em muitos outros campos. Neste contexto, abordamos a integral fracionária e as derivadas fracionárias, segundo Caputo e segundo Riemann-Liouville. Dentre as funções relacionadas ao cálculo fracionário, uma das mais importantes é a função de Mittag-Leffler, surgindo naturalmente na solução de várias equações diferenciais fracionárias com coeficientes constantes. Tendo em vista a importância dessa função, a clássica função de Mittag-Leffler e algumas de suas várias generalizações são apresentadas neste trabalho. Na aplicação resolvemos a equação diferencial associada ao problema do oscilador harmônico fracionário, utilizando a transformada de Laplace e a derivada fracionária segundo Caputo
Abstract: The fractional calculus, which is the nomenclature used to the non-integer order calculus, has important applications due to its direct involvement in problem resolution and discussion in many fields, such as mathematics, physics, engineering, economy, applied sciences and many others. In this sense, we studied the fractional integral and fractional derivates: one proposed by Caputo and the other by Riemann-Liouville. Among the fractional calculus's functions, one of most important is the Mittag-Leffler function. This function naturally occurs as the solution for fractional order differential equations with constant coeficients. Due to the importance of the Mittag-Leffler functions, various properties and generalizations are presented in this dissertation. We also presented an application in fractional calculus, in which we solved the differential equation associated the with fractional harmonic oscillator. To solve this fractional oscillator equation, we used the Laplace transform and Caputo fractional derivate
Mestrado
Matematica Aplicada
Mestra em Matemática Aplicada
Pedjeu, Jean-Claude. "Multi-time Scales Stochastic Dynamic Processes: Modeling, Methods, Algorithms, Analysis, and Applications." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4383.
Full textOliveira, Daniela dos Santos de 1990. "Derivada fracionária e as funções de Mittag-Leffler." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306994.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Neste trabalho apresentamos um estudo sobre as funções de Mittag-Leffler de um, dois e três parâmetros. Apresentamos a função de Mittag-Leffler como uma generalização da função exponencial bem como a relação que esta possui com outras funções especiais, tais como as funções beta, gama, gama incompleta e erro. Abordamos, também, a integração fracionária que se faz necessária para introduzir o conceito de derivação fracionária. Duas formulações para a derivada fracionária são estudadas, as formulações proposta por Riemann-Liouville e por Caputo. Investigamos quais regras clássicas de derivação são estendidas para estas formulações. Por fim, como uma aplicação, utilizamos a metodologia da transformada de Laplace para resolver a equação diferencial fracionária associada ao problema do oscilador harmônico fracionário
Abstract: This work presents a study about the one- two- and three-parameters Mittag-Leffler functions. We show that the Mittag-Leffler function is a generalization of the exponential function and present its relations to other special functions beta, gamma, incomplete gamma and error functions. We also approach fractional integration, which is necessary to introduce the concept of fractional derivatives. Two formulations for the fractional derivative are studied, the formulations proposed by Riemann-Liouville and by Caputo. We investigate which classical derivatives rules can be extended to these formulations. Finally, as an application, using the Laplace transform methodology, we discuss the fractional differential equation associated with the harmonic oscillator problem
Mestrado
Matematica Aplicada
Mestra em Matemática Aplicada
Miloš, Japundžić. "Uopštena rešenja nekih klasa frakcionih parcijalnih diferencijalnih jednačina." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2016. https://www.cris.uns.ac.rs/record.jsf?recordId=102114&source=NDLTD&language=en.
Full textColombeau spaces of generalized functions. In the firs part, we studied inhomogeneous evolution equations with space fractional differential operators of order 0 < α < 2 and variable coefficients depending on x and t. This class of equations is solved approximately, in such a way that instead of the originate equation we considered the corresponding approximate equation given by regularized fractional derivatives, i.e. their regularized multipliers. In the solving procedure we used a well-known generalized uniformly continuous semigroups of operators. In the second part, we solved approximately inhomogeneous fractional evolution equations with Caputo fractional derivative of order 0 < α < 2, linear, closed and densely defined operator in Sobolev space of integer order and variable coefficients depending on x. The corresponding approximate equation is a given by the generalized operator associated to the originate operator, while the solutions are obtained by using generalized uniformly continuous solution operators, introduced and developed for that purpose. In both cases, we provided the conditions that ensure the existence and uniqueness solutions of the Cauchy problem in some Colombeau spaces.
Kárský, Vilém. "Modelování LTI SISO systémů zlomkového řádu s využitím zobecněných Laguerrových funkcí." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2017. http://www.nusl.cz/ntk/nusl-316278.
Full textAhmad, Khan Mumtaz, and K. S. Nisar. "On a Generalizations of Lauricella’s Functions of Several Variables." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97061.
Full textEl presente artículo introduce 10 tipo de funciones generalizadas tipo Appell Ni, 1 ≤ i ≤ 10, considerando el producto de n funciones 3F2. El artículo contiene representaciones por derivadas fraccionales, representaciones integrales y formas simbólicas similares a aquellas obtenidas por J. L. Burchnall y T. W. Chaundy para las cuatro funciones de Appell, han sido obtenidas para estas nuevas funciones N1, N2.......N10. Los resultados parecen ser nuevos.
Oti, Vincent Bediako. "Numerické metody pro řešení počátečních úloh zlomkových diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445462.
Full textOuloin, Martyrs. "Méthode d’inversion d’un Modèle de diffusion Mobile Immobile fractionnaire." Thesis, Avignon, 2012. http://www.theses.fr/2012AVIG0504/document.
Full textAppealing models for mass transport in porous media assume that fluid and tracer particles can be trapped during random periods. Among them, the fractional version of the Mobile Immobile Model (f-MIM) was found to agree with several tracer test data recorded in environmental media.This model is equivalent to a stochastic process whose density probability function satisfies an advection-diffusion equation equipped with a supplementary time derivative, of non-integer order. The stochastic process is the hydrodynamic limit of random walks accumulating convective displacements, diffusive displacements, and stagnation steps of random duration distributed by a stable Lévy law having no finite average. Random walk and fractional differential equation provide complementary simulation methods.We describe that methods, in view of having tools for comparing the model with tracer test data consisting of time concentration curves. An other essential step in this direction is finding the four parameters of the fractional equation which make its solutions fit at best given sets of such data. Hence, we also present an inversion method adapted to the f-MIM. This method is based on Laplace transform. It exploits the link between model's parameters and Laplace transformed solutions to f-MIM equation. The link is exact in semi-infinite domains. After having checked inverse method's efficiency for numerical artificial data, we apply it to real tracer test data recorded in non-saturated porous sand
Punurai, Somrat. "Determinants of Outbound Cross-border Mergers and Acquisitions by Emerging Asian Acquirers." Thesis, University of North Texas, 2014. https://digital.library.unt.edu/ark:/67531/metadc700107/.
Full textCoja, Michael. "Effective vibro-acoustical modelling of rubber isolators." Doctoral thesis, Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-266.
Full textNenad, Grahovac. "Анализа дисипације енергије у проблемима судара два или више тела." Phd thesis, Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, 2011. http://dx.doi.org/10.2298/NS20111208GRAHOVAC.
Full textAnaliziran je sudar dva tela kao i disipacija energije uključena kroz mehanizam suvog trenja modeliranog neglatkom viševrednosnom funkcijom i kroz deformaciju viskoelastičnog štapa čiji model uključuje frakcione izvode. Problem sudara dva tela je prikazan u formi Košijevog problema koji pripada klasi neglatkih viševrednosnih diferencijalnih jednačina proizvoljnog realnogreda. Košijev problem je rešen numeričkim postupkom zasnovanim na Tarnerovom algoritmu. Ispitano je kretanje sistema i disipacija energije za razne vrednosti ulaznih parametara. Pokazano je da se uvedene metode mogu primeniti i na problem sudara tri tela.
Impact of two bodies was analyzed as well as energy dissipation, which was included through dry friction phenomena modelled by a set-valued function, and through deformation of a viscoelastic rod modelled by fractional derivatives. The impact problem was presented in the form of the Cauchy problem that belongs to a class of set-valued fractional differential equations. The Cauchy problem was solved by the numerical procedure based on Turner’s algorithm. Behaviour and energy dissipation of the system was investigated for different values of input parameters. It was shown that suggested procedure can be applied on the problem of impact of three bodies.
Fino, Ahmad. "Contributions aux problèmes d'évolution." Phd thesis, Université de La Rochelle, 2010. http://tel.archives-ouvertes.fr/tel-00437141.
Full textWiedmann, Steffen. "Nouvelles propriétés de transport dans les systèmes d'électrons multicouches." Thesis, Toulouse, INSA, 2010. http://www.theses.fr/2010ISAT0018/document.
Full textThis work is devoted to the investigation of the influence of the additional quantum degree of freedom caused by tunnel coupling on transport properties of multilayer electron systems in magnetic fields, at low temperatures and under microwave excitation. Microwave-induced resistance oscillations in bi- and multilayer electron systems are the consequence of an interference of magneto-intersubband and microwave-induced resistance oscillations which leads to peculiar oscillations in magnetoresistance. High-quality bilayer systems exposed to microwave irradiation exhibit zero-resistance states even in the presence of intersubband scattering. The inelastic mechanism of microwave photoresistance is found to be the dominant contribution at low temperatures and moderate microwave electric field. This model confirms the reliability of theoretical estimates for the inelastic relaxation time and leads to a satisfactory explanation of photoresistance in bi- and multilayer electron systems. In high magnetic fields, the suppression of tunnelling between layers causes new correlated states owing to electron-electron interaction in neighboured layers. In this thesis, trilayer electron systems formed by triple quantum wells reveal new fractional quantum Hall states if tunnelling is suppressed by a parallel component of the magnetic field at mK temperatures
Malik, Salman Amin. "Contributions aux équations aux dérivées fractionnaires et au traitement d'images." Phd thesis, Université de La Rochelle, 2012. http://tel.archives-ouvertes.fr/tel-00825874.
Full textDannawi, Ihab. "Contributions aux équations d'évolutions non locales en espace-temps." Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS007/document.
Full textIn this thesis, we study four non-local evolution equations. The solutions of these four equations can blow up in finite time. In the theory of nonlinear evolution equations, a solution is qualified as global if it isdefined for any time. Otherwise, if a solution exists only on a bounded interval [0; T), it is called local solution. In this case and when the maximum time of existence is related to a blow up alternative, we say that the solution blows up in finite time. First, we consider the nonlinear Schröodinger equation with a fractional power of the Laplacien operator, and we get a blow up result in finite time Tmax > 0 for any non-trivial non-negative initial condition in the case of sub-critical exponent. Next, we study a damped wave equation with a space-time potential and a non-local in time non-linear term. We obtain a result of local existence of a solution in the energy space under some restrictions on the initial data, the dimension of the space and the growth of nonlinear term. Additionally, we get a blow up result of the solution in finite time for any initial condition positive on average. In addition, we study a Cauchy problem for the evolution p-Laplacien equation with nonlinear memory. We study the local existence of a solution of this equation as well as a result of non-existence of global solution. Finally, we study the maximum interval of existence of solutions of the porous medium equation with a nonlinear non-local in time term
Imamovic, Arnela. "Cash is [no longer] king: is an e-krona the answer? : - a de lege ferenda investigation of the Swedish Riksbank's issuing mandate and other legal callenges in relation to economic effects on the payment market." Thesis, Linköpings universitet, Filosofiska fakulteten, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-156410.
Full textRakotonasy, Solonjaka Hiarintsoa. "Modèle fractionnaire pour la sous-diffusion : version stochastique et edp." Phd thesis, Université d'Avignon, 2012. http://tel.archives-ouvertes.fr/tel-00839892.
Full textChiao, Chien-Ying, and 喬建穎. "Random Vibration for Dynamical Systems with Fractional Derivatives." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/12505701870396658422.
Full text國立臺灣科技大學
營建工程系
102
This study presents an equivalent linear system approach for analying SDOF systems with fractional differential damping under nonstationary random excitations. The definition of the Riemann-Liouville fractional differential is adopted and the Newmark method is used as a tool for numerical analyses. The nonstationary excitations consider a Gaussian white noise process modulated by deterministic envelop functions. To approximate the displacement and velocity statistics, this paper uses deterministic steady-state responses for obtaining best equivalent stiffness and equivalent damping by which the original fractional differential system can then be replaced. In this framework,the traditional analytical methods such as the Liapunov Direct Method and the direct analytical method can then be directly executed. The study uses different values of damping ratio, fractional differential order and coefficient of strength to observe response differences between the approximated solutions and the Monte Carlo solutions. The results show that a reasonable precision level can be reached when the fractional coefficient is small.
Chen, Yu-Cheng, and 陳鈺承. "Numerical Analyses for Systems with Fractional Derivatives Dynamic." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/52352768531643616254.
Full text國立臺灣科技大學
營建工程系
101
This paper aims to study the fractional derivatives used in analysis of power system. This study is based on the definition of Riemann-Liouville fractional derivatives as the basis and introduced Newmark method to analyze the response of time history of dynamical systems. The study further use the dynamic system with a single degree of freedom to input different value of damping and fractional differential, and observe the response of free vibration;Finally, to analyze the response and differences of power system installed fractional damping system through 921 Taiwan Chi-Chi earthquake data. The results showed a rising value of fractional differential produce the trend transferred stiffness to damping of structure, with the increase in damping coefficient, and this trend will become more obvious. In addition, the use of response spectrum analysis found that the greater natural period, the more difference between the use of fractional and integer differential.
Wang, Yao-Min, and 王堯民. "Random Vibration Analysis of Dynamical Systems with Fractional Derivatives." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/92216319302959500350.
Full text國立臺灣科技大學
營建工程系
103
This paper aim to study under white Gaussian noise of stationary random process excitations, by changing coefficient of fractional derivatives , fractional differential order and damping ratio parameter to observe the response of equivalent system and Monte Carlo Simulation with fractional differential system , then analyze the errors between both systems. The results showed that when the fractional differential order and coefficient of fractional derivatives increased, the response of system will decay and will be steady state sooner, which represents the energy dissipation capacity of system will become more obvious, and which conforms that a rising value of fractional differential order produce the trend transferred stiffness to damping of structure ; when coefficient of fractional derivatives increased, the accuracy of the equivalent system will reduce, and the errors also increased along with fractional differential order in the beginning, when fractional differential order closed to the range 0.7~0.75, the maximum value of relative errors will even up to about 18%.
Chou, Tse-An, and 周澤安. "Random Vibration Analysis of Dynamical Systems with Fractional Derivatives." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/sb4d4u.
Full text國立臺灣科技大學
營建工程系
105
This study investigates stochastic responses of single-degree-of-freedom systems with a fractional differential damping subjected to white noise excitations. Both the unit impulse response function method and the Monte Carlo method are used to analyze the response differences. The mean square of the response displacements are studied through the variation of parameters, including the damping ratio, the fractional differential order, and the fractional differential coefficient. The results show that an increase in the fractional order will result in a response decrease with a faster rate in reaching steady states. This implies an enhancement of the energy dissipation capacity of the system due to a substantial increase in the effective damping. Moreover, when the fractional coefficient and fractional order are increased simultaneously, the response of the system would even decrease more significantly. It was found that the results based on the impulse function method and Monte Carlo method agree with each other. It’s concluded that both methods can substitute each other when only a linear system is considered.
Yu, Chun-Chieh, and 游竣傑. "Response of Free Vibration of Dynamical Systems with Fractional Derivatives." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/53443783416385973945.
Full text國立臺灣科技大學
營建工程系
104
This study presents a fundamental solution based on the Laplace transform method for a dynamical system with fractional derivatives. The system being investigated is a typical spring-mass system with an additional fractional order damping. This study also observes the response variations by changing the coefficient and the order of fractional derivatives, and the damping ratio parameter. The Caputo fractional derivative is assumed with an order α satisfying 0<α<1. The results show that the displacement responses exhibit ossillatory behavier with amplitude decaying over time. The displacement ultimately reaches zero in a smooth form. Addition to the displacement response, the associated velocity response is also presented. Where a similarly decayed ossillatory response type is observed.
Hung, Wei-Chi, and 洪偉齊. "An Analysis of Dynamical Systems with Fractional Derivatives Using Short Memory Principle." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/77306351083025056807.
Full text國立臺灣科技大學
營建工程系
102
This study presents an analysis of dynamical systems with fractional derivatives using the short memory principle. The study is based on the Remann-Liouville definition for the fractional derivative and the Newmark method is adopted to evaluate the responses. In this work, the response time history of a single-degree-of-freedom system is used as a comparison basis. The effects of different memory length and different fractional orders are identified by comparing the response differences between the short and full memory analyses. The feasibility of applying the short memory principle for response spectral analysis is also investigated where the 921 Taiwan Chi-Chi earthquake data are used as inputs. Study results show that under high fractional order, reasonable response accuracy can still be obtained when the short memory principle is applied.
Alsandor, Yvonne Renee U. "Deterministic and random vibrations of systems with frequency-dependent parameters or fractional derivatives." Thesis, 1998. http://hdl.handle.net/1911/17148.
Full text"Iterative determination of spar lines static equilibrium and improved dynamic modeling by fractional derivatives." Thesis, 2009. http://hdl.handle.net/1911/61843.
Full textSingh, Satwinder Jit. "New Solution Methods For Fractional Order Systems." Thesis, 2007. https://etd.iisc.ac.in/handle/2005/885.
Full textSingh, Satwinder Jit. "New Solution Methods For Fractional Order Systems." Thesis, 2007. http://hdl.handle.net/2005/885.
Full textFonseca, Mafalda Seco da. "Soluções numéricas para um problema de difusão de Knudsen." Master's thesis, 2018. http://hdl.handle.net/10316/86636.
Full textUm processo de difusão é caracterizado pelo transporte de matéria devido ao movimento aleatório das moléculas. A difusão de Knudsen é um processo de difusão anómalo que ocorre em meios porosos, onde o transporte de matéria é efetuado maioritariamente pela colisão das moléculas com as paredes do meio. Nesta dissertação apresentamos um modelo que envolve difusão anómala. Este modelo é descrito por uma equação integro-diferencial que envolve um operador diferencial, que é uma derivada fracionária de Riemann-Liouville no tempo. A solução analítica de equações que utilizam derivadas fracionárias não é fácil de obter analiticamente e, por isso, é necessário recorrer a métodos numéricos com vista a encontrar soluções aproximadas. Vamos apresentar essencialmente dois métodos numéricos, um explícito e um implícito no tempo. A derivada fracionária é aproximada pela denominada fórmula de Grünwald-Letnikov. Estes métodos numéricos só terão interesse se forem estáveis e convergirem para a solução exata, pelo que a sua convergência é analisada através da análise de Fourier e do método da energia.
A diffusion process is characterized by the transport of matter as a result of random molecular motion. Knudsen diffusion is a anomalous diffusion process, which occurs in porous media, and where the transport of matter is mostly due to the collision of molecules with he inside walls. In this thesis, we present a model that involves anomalous diffusion. It is described by a integro-differential equation, which involves the Riemann-Liouville fractional derivative in time. The analytical solution of equations that involve fractional derivatives are difficult to obtain and therefore, we need to use numerical methods in order to find approximate solutions. We will present two numerical methods, an implicit and an explicit in time. The fractional derivative is approximated by Grünwald-Letnikov formula. These numerical methods need to be stable and converge to the exact solution. Hence the convergence and stability of the numerical methods are studied through the Fourier analysis and the energy method.