A numerical method for finding solution of the distributed‐order time‐fractional forced Korteweg–de Vries equation including the Caputo fractional derivative [PDF]
Mathematical Methods in the Applied Sciences, 2020 In this paper, for the first time, the distributed‐order time‐fractional forced Korteweg–de Vries equation is studied. We use a numerical method based on the shifted Legendre operational matrix of distributed‐order fractional derivative with Tau method to find approximate solution of distributed‐order forced Korteweg–de Vries equation.
Mohammad Hossein Derakhshan +1 more
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On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory
Fractal and Fractional, 2023 A novel two-compartment model for drug release was formulated. The general fractional derivatives of a specific type and distributed order were used in the formulation. Earlier used models in pharmacokinetics with fractional derivatives follow as special
Vesna Miskovic-Stankovic +1 more
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Frontiers in Physics, 2020 Distributed-order fractional differential operators provide a powerful tool for mathematical modeling of multiscale multiphysics processes, where the differential orders are distributed over a range of values rather than being just a fixed fraction.
Ramy M. Hafez +3 more
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Axioms, 2015 This article is in continuation of the authors research attempts to derive computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as ...
Ram K. Saxena +2 more
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Maximum Principle and Its Application for the Time-Fractional Diffusion Equations [PDF]
, 2011 MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversaryIn the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion ...
Luchko, Yury
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A Plea for the Integration of Fractional Differential Systems: The Initial Value Problem
Fractal and Fractional, 2022 The usual approach to the integration of fractional order initial value problems is based on the Caputo derivative, whose initial conditions are used to formulate the classical integral equation.
Nezha Maamri, Jean-Claude Trigeassou
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Consensus of Multiagent Systems Described by Various Noninteger Derivatives
Complexity, 2019 In this paper, we unify and extend recent developments in Lyapunov stability theory to present techniques to determine the asymptotic stability of six types of fractional dynamical systems.
G. Nava-Antonio +4 more
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Generalized distributed order diffusion equations with composite time fractional derivative
Computers & Mathematics with Applications, 2017 Computers and Mathematics with Applications (2016)
Trifce Sandev +2 more
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Delay-Dependent Stability Criterion of Caputo Fractional Neural Networks with Distributed Delay
Discrete Dynamics in Nature and Society, 2014 This paper is concerned with the finite-time stability of Caputo fractional neural networks with distributed delay. The factors of such systems including Caputo’s fractional derivative and distributed delay are taken into account synchronously.
Abdulaziz Alofi +3 more
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Controllability of higher-order fractional damped stochastic systems with distributed delay
Advances in Difference Equations, 2021 In this paper, the controllability analysis is proposed for both linear and nonlinear higher-order fractional damped stochastic dynamical systems with distributed delay in Hilbert spaces which involve fractional Caputo derivative of different orders ...
G. Arthi, K. Suganya, Yong-Ki Ma
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