TITLE:
Multiple Solutions for a Class of Singular Boundary Value Problems of Hadamard Fractional Differential Systems with p-Laplacian Operator
AUTHORS:
Chen Wang, Yansheng Liu
KEYWORDS:
Multiple Solutions, Fixed Point Index Theory, Nonlinear Fractional Differential Systems, Hadamard Fractional Derivative
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.9,
September
20,
2024
ABSTRACT: This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.