Existence and Uniqueness of Solutions for Nonlinear Ψ ‐Liouville–Caputo–Katugampola Fractional Integro‐Differential Equations

This paper studies a nonlinear hybrid Ψ ‐Liouville–Caputo–Katugampola fractional integro‐differential equation. The proposed problem contains functional, Volterra integral, and delay terms. First, we derive the corresponding fractional integral equation. The problem is studied in the Banach algebra endowed with the supremum norm. Under suitable Lipschitz and boundedness assumptions on the nonlinear terms, we establish the existence of solutions by using Dhage′s fixed‐point theorem. Under stronger Lipschitz conditions, the uniqueness of the solution is obtained by applying the Banach contraction principle. Finally, an example is presented to show that the assumptions and conditions of the obtained results can be satisfied.