Existence and Compactness of the Solution Set for a Coupled Caputo Fractional System with ϕ-Laplacian Operators and Nonlocal Boundary Conditions

In this paper, we investigate a class of coupled fractional differential systems involving Caputo derivatives and nonlinear ϕ-Laplacian operators subject to nonlocal boundary conditions. By transforming the problem into an equivalent integral system via appropriate Green’s functions, the existence of solutions is studied within a generalized Banach space framework. Using a Leray–Schauder type fixed point theorem and suitable growth conditions on the nonlinear terms, we establish the existence of at least one bounded solution. Furthermore, we prove that the solution set is compact. An illustrative example involving the p-Laplacian operator is provided to demonstrate the applicability of the obtained theoretical results.