Existence of solutions for fractional functional integral equations of Hadamard type via measure of noncompactness

In this paper, we study the solvability for fractional functional integral equations of Hadamard-type within the Banach algebra \(C([1, c]), c > 0\) $C([1,c]),c>0$ . We utilize the Darbo’s fixed point theorem combined with the measure of non-compactness as the main tool. Notably, our existence results encompass and generalize various findings documented in previous literature. To demonstrate the applicability of our approach, we present a detailed example highlighting its effectiveness.