Existence of solution for infinite system of fractional differential equation in the sequence space n(ϕ) using Meir-Keeler condensing operator

Abstract

In this paper, we investigate the existence of solutions of an infinite system of fractional differential equations in the sequence spaces n(ϕ). We use the Meir-Keeler condensing operator concept in conjunction with the Hausdorff measure of noncompactness to study the solvability, and we include suitable examples to demonstrate our findings. Additionally, we incorporate a combined semi-analytical method of modified Homotopy Perturbation Method along with the Adomian Decomposition Method to approximate solutions for the system. The examples presented further substantiate the effectiveness of the proposed approach while enabling practical estimation of solutions to the infinite system.