A numerical method for solving a class of nonlinear second order fractional Volterra integro-differntial type of singularly perturbed problems
type: Item
instance of: scholarly article
title: A numerical method for solving a class of nonlinear second order fractional Volterra integro-differntial type of singularly perturbed problems
zbMATH Open document ID: 1448.65286
author: Muhammed Syam
author: Mohammed Abu Omar
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: In this paper, we study a class of fractional nonlinear second order Volterra integro-differential type of singularly perturbed problems with fractional order. We divide the problem into two subproblems. The first subproblems is the reduced problem when \(\epsilon =0\). The second subproblem is a fractional Volterra integro-differential problem. We use the finite difference method to solve the first problem and the reproducing kernel method to solve the second problem. In addition, we use Pade' approximation. The results show that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. Theoretical results are presented. Numerical results are presented to show the efficiency of the proposed method.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 6898740
zbMATH Keywords: singularly perturbed Volterra integro-differntial equation
zbMATH Keywords: Caputo fractional derivative
zbMATH Keywords: nonlinear boundary value problem
MaRDI profile type: Publication
full work available at URL: math6040048
OpenAlex ID: W2795357934
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Wikidata QID: Q130111645
DOI: 10.3390/MATH6040048
description: scientific article; zbMATH DE number 6898740