Stability and Existence Analysis To a Coupled System of Caputo Type Fractional Differential Equations With Erdelyi-Kober Integral Boundary Conditions

Abstract

This article focuses on the Hyers-Ulam type stability, existence and uniqueness of solutions for new types of coupled boundary value problems involving fractional differential equations of Caputo type and augmented with Erdelyi-Kober fractional integral boundary conditions. The nonlinearity relies on the unknown functions. The consequence of the existence is obtained through the Leray-Schauder alternative, whereas the uniqueness of the solution relies on the Banach contraction mapping principle.We analyze the stability of the solutions concerned in the Hyers-Ulam form. As an application, some examples are presented to illustrate the main results. Finally, some variants of the problem are addressed. © 2020 NSP Natural Sciences Publishing Cor.