On the approximate solutions of a class of fractional order nonlinear Volterra integro-differential initial value problems and boundary value problems of first kind and their convergence analysis
On the approximate solutions of a class of fractional order nonlinear Volterra integro-differential initial value problems and boundary value problems of first kind and their convergence analysis
Das, Pratibhamoy 1Rana, Subrata 1Ramos, Higinio2
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作者信息
1. Indian Inst Technol
2. Univ Salamanca
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Abstract
In this work we consider a class of fractional order Volterra integro-differential equations of first kind where the fractional derivative is considered in the Caputo sense. Here, we consider the initial value problem and the boundary value problem separately. For simplicity of the analysis, we reduce each of these problems to the fractional order Volterra integro-differential equation of second kind by using the Leibniz's rule. We have obtained sufficient conditions for the existence and uniqueness of the solutions of initial and the boundary value problems. An operator based method has been considered to approximate their solutions. In addition, we provide a convergence analysis of the adopted approach. Several numerical experiments are presented to support the theoretical results. (c) 2020 Elsevier B.V. All rights reserved.
Key words
Fractional integro differential equation/Volterra differential equation of first kind/Existence and uniqueness/Perturbation based approximation/Homotopy perturbation/Convergence analysis/NUMERICAL-SOLUTION/EQUATIONS/MESHES
NSTL
Elsevier