Solvability of $(P,Q)$-functional integral equations of fractional order using generalized Darbo's fixed point theorem

Abstract

In this article, we establish a generalized version of Darbo's fixed point theorem via some newly defined condensing operators and we define a new fractional integral using $(P,Q)$-calculus and study its properties.
Finally, we apply this generalized Darbo's fixed point theorem to check the existence of solution of $(P,Q)$-functional integral equations of fractional order in a Banach space. We explain the results with the help of simple examples.