Positive Solutions for a System of Hadamard Fractional Boundary Value Problems on an Infinite Interval

Abstract

Our investigation is devoted to examining the existence, uniqueness, and multiplicity of positive solutions for a system of Hadamard fractional differential equations. This system is defined on an infinite interval and is subject to coupled nonlocal boundary conditions. These boundary conditions encompass both Hadamard fractional derivatives and Riemann–Stieltjes integrals, and the nonlinearities within the system are non-negative functions that may not be bounded. To establish the main results, we rely on the utilization of mathematical theorems such as the Schauder fixed-point theorem, the Banach contraction mapping principle, and the Avery–Peterson fixed-point theorem.

Keywords

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