Fractal and Fractional (Apr 2024)
Study on a Nonlocal Fractional Coupled System Involving (<i>k</i>,<i>ψ</i>)-Hilfer Derivatives and (<i>k</i>,<i>ψ</i>)-Riemann–Liouville Integral Operators
Abstract
This paper deals with a nonlocal fractional coupled system of (k,ψ)-Hilfer fractional differential equations, which involve, in boundary conditions, (k,ψ)-Hilfer fractional derivatives and (k,ψ)-Riemann–Liouville fractional integrals. The existence and uniqueness of solutions are established for the considered coupled system by using standard tools from fixed point theory. More precisely, Banach and Krasnosel’skiĭ’s fixed-point theorems are used, along with Leray–Schauder alternative. The obtained results are illustrated by constructed numerical examples.
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