Existence and Extremal Solution for Fractionalorder Nonlinear Integro-Differential Equation in Banach Algebras

Abstract

In this Paperwe study theexistence the solution for a fractional order nonlinear integro-differential equation in Banach Algebras.Wemake use of the standard tools of the hybrid fixed Point theory for three operators to establish the main result. We also proved theexistence solutionsare locally attractive in and extremal result are also proved. Finally, our results are illustrated by a concrete example.