ON RANDOM FRACTIONAL DIFFERENTIAL COUPLED SYSTEMS WITH HILFER–KATUGAMPOLA FRACTIONAL DERIVATIVE IN BANACH SPACES.

This paper delves into the investigation of existence and uniqueness results concerning the Hilfer–Katugampola random nonlinear fractional differential coupled system within a generalized Banach space. Such problems represent a broadened scope, extending several existing results in the literature and offering potential avenues for furthering the development of this evolving theory. Our findings are derived through the application of various random fixed point theorems, including Banach’s random fixed point theorem, the random nonlinear alternative of the Leray–Schauder type, and Schauder’s random fixed point theorem. To validate our results, an illustrative example is presented in the final section. [ABSTRACT FROM AUTHOR]