Analysis of nonlinear implicit coupled Hadamard fractional differential equations with semi-coupled Hadamard fractional integro-multipoints boundary conditions

Abstract

The study is devoted to demonstrating the hypothesis necessary for the existence, uniqueness and at least one solution of implicit Hadamard fractional differential equations with nonlocal semi-coupled fractional integro-multipoints boundary conditions. Using Banach contraction principle, the uniqueness result is obtained. Leray–Schauder fixed point theorem supports the results of at least one solution of the aforementioned system. Additionally, By two different approaches, Hyers–Ulam stabilities are discussed for the proposed system. For verification, an example is presented. Through Remarks, ordinary differential equation of second-order with periodic and initial conditions are given by fixing some parameters in the suggested system.