Solvability of Implicit Fractional Systems With Nonlocal Conditions in Weighted Functional Spaces

This paper investigates the existence and uniqueness of solutions for a class of nonlinear implicit Riemann–Liouville fractional integro-differential equations subject to nonlocal conditions in a weighted Banach space. The inclusion of both implicit effects and nonlocal terms introduces additional complexity, making the analysis both challenging and interesting from a theoretical perspective. To establish our main results, we employ a combination of classical fixed point theorems, including the Banach contraction principle and Krasnoselskii’s fixed point theorem. These tools provide a robust framework for handling the nonlinearities and integral terms inherent in the problem. Furthermore, to illustrate the applicability and effectiveness of the theoretical findings, we present a detailed example. This example not only validates the theoretical framework but also demonstrates how the abstract results can be applied to concrete problems.