ON SOLVABILITY AND APPROXIMATING THE SOLUTIONS FOR NONLINEAR INFINITE SYSTEM OF FRACTIONAL FUNCTIONAL INTEGRAL EQUATIONS IN THE SEQUENCE SPACE ℓp, p>1

Abstract

We studied a new class of nonlinear infinite system of functional integral equations with Riemann–Liouville fractional operator and their existing solution in the sequence space ${\ell }_p$, $p>1$. We first prove the existence of a solution for the infinite system of functional integral equation by using Hausdorff measure of noncompactness and the generalized Meir–Keeler fixed-point theorem. Also, we have presented an example to illustrate the effectiveness of our main result. Further, we propose an iterative algorithm formed by homotopy perturbation along with the Adomian decomposition method to solve the considered problem with acceptable accuracy, which converges strongly to the approximate solution.