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The Laplace Transform Method for Linear Differential Equations of the Fractional Order [PDF]
In modified form included in Chapters 4 and 5 of the book:
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego,
1999, 368 pages, ISBN 0125588402., 1997 The Laplace transform method for solving of a wide class of initial value problems for fractional differential equations is introduced. The method is based on the Laplace transform of the Mittag-Leffler function in two parameters. To extend the proposed method for the case of so-called "sequential" fractional differential equations, the Laplace ...
Igor Podlubný
arxiv +3 more sources
Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
Advances in Mathematical Physics, 2021 By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional ...
Chao Yue +3 more
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AIMS Mathematics, 2022 Based on the variable separation method, the Kadomtsev-Petviashvili equation is transformed into a system of equations, in which one is a fractional ordinary differential equation with respect to time variable t, and the other is an integer order ...
Cheng Chen
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Abstract and Applied Analysis, 2010 The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has ...
Coşkun Yakar
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Fractional Differential Equations [PDF]
, 2019 Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different ...
Juan J. Nieto, Rosana Rodríguez-López
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Fractional Differential Equations 2012 [PDF]
International Journal of Differential Equations, 2013 Journal of Differential Equations dédié aux équations différentielles fractionnaires (FDE). Ces dernières années, un nombre croissant d'articles rédigés par de nombreux auteurs de divers domaines de la science et de l'ingénierie traitent de systèmes dynamiques décrits par des équations aux dérivées partielles fractionnaires.
Fawang Liu +4 more
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Advances in Mathematical Physics, 2019 The motivation of this study is to construct the truncated solution of space-time fractional differential equations by the homotopy analysis method (HAM).
Ali Demir +2 more
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Stability analysis of multi-term fractional-differential equations with three fractional derivatives [PDF]
, 2020 Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases, fractional-order-dependent as well as fractional-order-independent characterisations of stability and instability properties are obtained ...
arxiv +1 more source
Nonlocal Fractional Differential Equations and Applications [PDF]
Complex Analysis and Operator Theory, 2020 Boundary value problems for nonlocal fractional elliptic equations with parameter in Banach spaces are studied. Uniform $L_p$-separability properties and sharp resolvent estimates are obtained for elliptic equations in terms of fractional derivatives.
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Existence of fractional differential equations
Journal of Mathematical Analysis and Applications, 2005 AbstractConsider the fractional differential equation Dαx=f(t,x), where α∈(0,1) and f(t,x) is a given function. We obtained a sufficient condition for the existence for the solutions of this equation, improving previously known results.
Cheng Yu, Guozhu Gao
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