On solution of generalized proportional fractional integral via a new fixed point theorem

Abstract

The aim of this paper is the solvability of generalized proportional fractional(GPF) integral equation at Banach space $\mathbb{E}$ E . Herein, we have established a new fixed point theorem which is then applied to the GPF integral equation in order to establish the existence of solution on the Banach space. At last, we have illustrated a genuine example that verified our theorem and gave a strong support to prove it.