Investigating positive solutions in $p$-Laplacian fractional systems with infinite-point boundaries

This study explored the theoretical characteristics of a $p$-Laplacian fractional-order differential equation. This equation was subject to both infinite-point boundary value requirements and nonlocal integral value constraints. We began by examining the associated Green's function, deriving its explicit expression and unique properties. These properties were then utilized to establish the existence and uniqueness of positive solutions through the application of the Banach fixed-point technique. Furthermore, we employed the nonlinear alternative of Leray-Schauder type, specifically Guo-Krasnoselskii's fixed-point theorem on cones, to demonstrate existence results for cases where the nonlinearity exhibits singularity with respect to the time variable. The practical relevance and applicability of our findings were illustrated through compelling examples. This research significantly contributed to the field of fractional differential equations, particularly within the domain of $p$-Laplacian Hadamard fractional differential equations.