INVESTIGATION OF A NEW COUPLED SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS IN FRAME OF HILFER-HADAMARD

Abstract

The primary focus of this paper is to thoroughly examine and analyze a coupled system by a Hilfer-Hadamard-type fractional differential equation with coupled boundary conditions. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the problem, effectively transforming the given system into an equivalent fixed-point problem. The necessary conditions for the existence and uniqueness of solutions for the system are established using Banach’s fixed point theorem and Schaefer’s fixed point theorem. An illustrate example is presented to demonstrate the effectiveness of the developed controllability results.