Solvability for 2D non-linear fractional integral equations by Petryshyn's fixed point theorem

This paper explores a 2D non-linear fractional integral equation of the Riemann-Liouville type. The authors establish the existence of at least one solution for this 2D integral equation in the Banach space of all real continuous functions on [0, c] x [0, d], under some weaker conditions. The main tools used in our considerations are the concept of a measure of noncompactness and Petryshyn's fixed point theorem. Illustrative examples highlight the broad applicability of our findings across a diverse spectrum of integral equations.