An Analytical Survey on the Solutions of the Generalized Double-Order <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>φ</a:mi> </a:math>-Integrodifferential Equation

Abstract

We study the existence of solutions for a newly configured model of a double-order integrodifferential equation including <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:mi>φ</a:mi> </a:math> -Caputo double-order <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M3"> <c:mi>φ</c:mi> </c:math> -integral boundary conditions. In this way, we use the Krasnoselskii and Leray-Schauder fixed point results. Also, we invoke the Banach contraction principle to confirm the uniqueness of the existing solutions. Finally, we provide three examples to illustrate our analytical findings.

Topics & Concepts