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


Anupam Das, Bipan Hazarika, Mohammad Mursaleen, Hemant Kumar Nashine, Vahid Parvaneh




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 a solution of (P, Q)-functional integral equations of fractional order in a Banach space. We explain the results with the help of simple examples.