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Título
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
Autor(es)
Materia
Fractional integro differential equation
Volterra differential equation of first kind
Existence and uniqueness
Perturbation based approximation
Homotopy perturbation
Convergence analysis
Clasificación UNESCO
12 Matemáticas
1299 Otras Especialidades Matemáticas
Fecha de publicación
2022
Editor
Elsevier
Resumen
[EN]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.
URI
ISSN
0377-0427
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