Existence Results for a Nonlocal Coupled System of Sequential Fractional Differential Equations Involving <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>ψ</a:mi> </a:math>-Hilfer Fractional Derivatives

Abstract

In this article, we discuss the existence and uniqueness of solutions for a new class of coupled system of sequential fractional differential equations involving <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:mi>ψ</a:mi> </a:math> -Hilfer fractional derivatives, supplemented with multipoint boundary conditions. We make use of Banach’s fixed point theorem to obtain the uniqueness result and the Leray-Schauder alternative to obtain the existence result. Examples illustrating the main results are also constructed.

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