On the Solvability of Mixed-Type Fractional-Order Non-Linear Functional Integral Equations in the Banach Space C(I)

Abstract

This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional ((Formula presented.))-Riemann–Liouville along with Erdélyi–Kober fractional operators on a Banach space (Formula presented.) arising in biological population dynamics. The key findings of the article are based on theoretical concepts pertaining to the fractional calculus and the Hausdorff measure of non-compactness (MNC). To obtain this goal, we employ Darbo’s fixed-point theorem (DFPT) in the Banach space. In addition, we provide two numerical examples to demonstrate the applicability of our findings to the theory of fractional integral equations