The existence analysis of new class of fractional differential equation

Abstract

In this article, we present a new class of nonlinear differential equations and prove the existence and uniqueness of their solutions. The proof is based on applying Krasnoselskii’s fixed-point theorem and Banach’s Contraction Mapping Theorem. We establish sufficient conditions for the existence of solutions within an appropriate Banach space and show that these solutions are unique. The combination of these two powerful theorems allows us to address the challenges posed by the nonlinear nature of the equations. Additionally, we provide an illustrative example to demonstrate the practical application of our results. The approach presented not only advances the theoretical understanding of nonlinear differential equations but also offers a robust framework for solving such equations in various applied settings.