Discretization of Fractional Differential Equations by a Piecewise Constant Approximation
, 2016 There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a dynamical ...
Angstmann, Christopher N +2 more
core
Fredholm boundary-value problem for the system of fractional differential equations. [PDF]
Nonlinear Dyn, 2023 Boichuk O, Feruk V.
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On fractional Duhamel's principle and its applications [PDF]
arXiv, 2010 The classical Duhamel principle, established nearly 200 years ago by Jean-Marie-Constant Duhamel, reduces the Cauchy problem for an inhomogeneous partial differential equation to the Cauchy problem for the corresponding homogeneous equation. Duhamel's principle is not applicable in the case of fractional order differential equations.
arxiv
Existence of deviating fractional differential equation [PDF]
Cubo (Temuco), 2012 In this paper we shall establish sufficient conditions for the existence of solutions of a class of fractional differential equation (Cauchy type ) and its solvability in a subset of the Banach space. The main tool used in our study is the non-expansive operator technique. The non integer case is taken in sense of Riemann Liouville fractional operators.
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Stability of some generalized fractional differential equations in the sense of Ulam-Hyers-Rassias. [PDF]
Bound Value Probl, 2023 Makhlouf AB +4 more
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Series expansion in fractional calculus and fractional differential equations [PDF]
arXiv, 2009 Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus.
arxiv
Implementation of non-linear mixed effects models defined by fractional differential equations. [PDF]
J Pharmacokinet Pharmacodyn, 2023 Kaikousidis C, Dokoumetzidis A.
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Flow properties of differential equations driven by fractional Brownian motion [PDF]
arXiv, 2006 We prove that solutions of stochastic differential equations driven by fractional Brownian motion for $H>1/2$ define flows of homeomorphisms on $\mathbb{R}^{d}$.
arxiv
Author Correction: Deterministic-stochastic analysis of fractional differential equations malnutrition model with random perturbations and crossover effects. [PDF]
Sci Rep, 2023 Chu YM +4 more
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A new Bihari inequality and initial value problems of first order fractional differential equations. [PDF]
Fract Calc Appl Anal, 2023 Lan K, Webb JRL.
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