Positive Solutions to a System of Coupled Hadamard Fractional Boundary Value Problems

Abstract

We explore the existence, uniqueness, and multiplicity of positive solutions to a system of Hadamard fractional differential equations that contain fractional integral terms. Defined on a finite interval, this system is subject to general coupled nonlocal boundary conditions encompassing Riemann–Stieltjes integrals and Hadamard fractional derivatives. To establish the main results, we employ several fixed-point theorems, namely the Banach contraction mapping principle, the Schauder fixed-point theorem, the Leggett–Williams fixed-point theorem, and the Guo–Krasnosel’skii fixed-point theorem.

Keywords

• Hadamard fractional differential equations
• nonlocal coupled boundary conditions
• existence
• uniqueness
• multiplicity
• positive solutions