Existence and Uniqueness Analysis for (k, ψ)-Hilfer and (k, ψ)-Caputo Sequential Fractional Differential Equations and Inclusions with Non-Separated Boundary Conditions - Furkan Erkan; Nuket Aykut Hamal; Sotiris K. Ntouyas; Jessada Tariboon (Fractal and Fractional, 2025)
This paper investigates the existence and uniqueness of solutions to a class of sequential fractional differential equations and inclusions involving the <semantics>(k,ψ)</semantics>-Hilfer and <semantics>(k,ψ)</semantics>-Caputo derivatives under non-separated boundary conditions. By reformulating the problems into equivalent fixed-point systems, several classical fixed-point theorems, including those of Banach, Krasnosel’ski<semantics><mover>i˘</mover></semantics>’s, Schaefer, and the Leray–Schauder alternative, are employed to derive rigorous results. The study is further extended to the multi-valued setting, where existence results are established for both convex- and nonconvex-valued multi-functions using appropriate fixed-point techniques. Numerical examples are provided to illustrate the applicability and effectiveness of the theoretical findings.