A Hadamard Fractional Boundary Value Problem on an Infinite Interval at Resonance

Abstract

This paper addresses the existence of solutions to a Hadamard fractional differential equation of arbitrary order on an infinite interval, subject to integral boundary conditions that incorporate both Riemann–Stieltjes integrals and Hadamard fractional derivatives. Due to the presence of nontrivial solutions in the associated homogeneous boundary value problem, the problem is classified as resonant. The Mawhin continuation theorem is utilized to derive the main findings.

Keywords

• Hadamard fractional differential equation
• integral boundary conditions
• existence of solutions
• resonant problem