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

Abstract

Abstract The aim of this paper is the solvability of generalized proportional fractional(GPF) integral equation at Banach space E $\mathbb{E}$ . 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.

Keywords

• Measure of noncompactness (MNC)
• Fixed point theorem
• Generalized proportional fractional integral