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Approximations of fractional integrals and Caputo fractional derivatives
Applied Mathematics and Computation, 2006In a series of recent papers [see \textit{K. Diethelm, A. D. Freed} and \textit{N. J. Ford}, Numer. Algorithms 36, No. 1, 31--52 (2004; Zbl 1055.65098)], and the references cited therein], the reviewer and his collaborators have proposed and analysed a numerical scheme for the approximation of \(J^\alpha\), the Riemann-Liouville fractional integral of ...
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To the Theory of Differential Inclusions with Caputo Fractional Derivatives
Differential Equations, 2020The paper studies a Cauchy problem associated to fractional differential inclusions of the form \[ ^CD^{\alpha }x(t)\in F(t,x(t)),\quad a.e.\; t\in [t_0,T], \] \[ x(t)=w_0(t),\quad t\in [0,t_0], \] where \(\alpha \in (0,1)\), \(^CD^{\alpha }\) denotes Caputo's fractional derivative, \(F:[0,T]\times {\mathbb{R}}^n\to \mathcal{P}({\mathbb{R}}^n)\) is a ...
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Generating Functions and Approximations of the Caputo Fractional Derivative
2023Yuri Dimitrov +4 more
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Communications in Nonlinear Science and Numerical Simulation, 2020
Luisa Beghin, Michele Caputo
exaly
Luisa Beghin, Michele Caputo
exaly
Stability Analysis of a Fractional-Order Linear System Described by the Caputo–Fabrizio Derivative
Mathematics, 2019Jun Cheng, Hou-Biao Li
exaly
Fundamental results on weighted Caputo–Fabrizio fractional derivative
Chaos, Solitons and Fractals, 2019Mohammed Al-Refai
exaly
Modeling non-Darcian flow and solute transport in porous media with the Caputo–Fabrizio derivative
Applied Mathematical Modelling, 2019H W Zhou
exaly