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Analysis of fractional Fokker-Planck equation with Caputo and Caputo-Fabrizio derivatives
Annals of the University of Craiova - Mathematics and Computer Science Series, 2021This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained.
Suleyman Cetinkaya +2 more
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Caputo fractional derivative of $$\alpha $$-fractal spline
Numerical AlgorithmszbMATH Open Web Interface contents unavailable due to conflicting licenses.
T. M. C. Priyanka +4 more
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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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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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Communications in Nonlinear Science and Numerical Simulation, 2020
Luisa Beghin, Michele Caputo
exaly
Luisa Beghin, Michele Caputo
exaly
Generating Functions and Approximations of the Caputo Fractional Derivative
2023Yuri Dimitrov +4 more
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Caputo and Atangana-Baleanu-Caputo Fractional Derivative Applied to Garden Equation
2020In this study, the garden equation which is a nonlinear partial differential equation is discussed. First, we will expand the garden equation to the Caputo derivative and Atangana-Baleanu fractional derivative in the sense of Caputo. Then, we will then demonstrate the existence of the new equation with the help of the fixed point theorem.
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Stability Analysis of a Fractional-Order Linear System Described by the Caputo–Fabrizio Derivative
Mathematics, 2019Jun Cheng, Hou-Biao Li
exaly