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Discontinuity, Nonlinearity, and Complexity 12(3) (2023) 701--714 | DOI:10.5890/DNC.2023.09.015

Vijai Kumar Pathak, Lakshmi Narayan Mishra

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014,

Tamil Nadu, India

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Abstract

In the present study, our main work is focused on solving the fractional order nonlinear infinite system of Erd$\acute{\mbox{e}}$lyi-Kober type functional integral equations in sequence space $\ell_p,~ p>1$ by applying Hausdorff measure of non-compactness, and generalized Meir-Keeler (M-K) fixed point theorem. An example is presented to validate our existence theorem. We propose an iterative algorithm formed by homotopy perturbation along with the Adomian decomposition method to solve the considered problem with high accuracy. A numerical example is also used to show that our iterative algorithm converges strongly to the approximate solution of the proposed problem.

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