Aziz Khan

On Coupled p-Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions

This paper is related to the existence and uniqueness of solutions to a coupled system of fractional differential equations (FDEs) with nonlinear -Laplacian operator by using fractional integral boundary conditions with nonlinear term and also to checking the Hyers-Ulam stability for the proposed problem. The functions involved in the proposed coupled system are continuous and satisfy certain growth conditions. By using topological degree theory some conditions are established which ensure the existence and uniqueness of solution to the proposed problem. Further, certain conditions are developed corresponding to Hyers-Ulam type stability for the positive solution of the considered coupled system of FDEs. Also, from applications point of view, we give an example.

Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential Equations

We discuss existence, uniqueness, and Hyers-Ulam stability of solutions for coupled nonlinear fractional order differential equations (FODEs) with boundary conditions. Using generalized metric space, we obtain some relaxed conditions for uniqueness of positive solutions for the mentioned problem by using Perov’s fixed point theorem. Moreover, necessary and sufficient conditions are obtained for existence of at least one solution by Leray-Schauder-type fixed point theorem. Further, we also develop some conditions for Hyers-Ulam stability. To demonstrate our main result, we provide a proper example.