A STUDY OF COUPLED FRACTIONAL INTEGRODIFFERENTIAL SYSTEMS IN THE TEMPERED (K, φ)-HILFER FRAMEWORK WITHIN BANACH SPACES

This work investigates a class of nonlinear coupled fractional integrodifferential systems formulated in the tempered $ (k,\varphi) $-Hilfer framework. The analysis is conducted within an infinite-dimensional Banach space, where the nonlinear components are assumed to satisfy a blend of compactness and growth conditions. Employing the Mönch fixed-point theorem in conjunction with the measure of noncompactness, we establish an existence result that significantly generalizes and strengthens several existing results in the literature. To illustrate the applicability of the theoretical results, a representative example is provided in an infinite-dimensional Banach space setting.