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

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 redu...

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Vydané v:Journal of computational and applied mathematics Ročník 404; s. 113116
Hlavní autori: Das, Pratibhamoy, Rana, Subrata, Ramos, Higinio
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.04.2022
Predmet:
Convergence analysis
Existence and uniqueness
Fractional integro differential equation
Homotopy perturbation
Perturbation based approximation
Volterra differential equation of first kind
34A12
26A33
Fractional integro differential equation
34K37
Perturbation based approximation
34A08
Convergence analysis
Homotopy perturbation
41A58
34K09
34K06
34K28
34A10
Volterra differential equation of first kind
Existence and uniqueness
ISSN:0377-0427, 1879-1778
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Popis
Shrnutí: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2020.113116