Existence results for a class of nonlinear singular p-Laplacian Hadamard fractional differential equations

Abstract

Based on properties of Green's function and the some conditions of $ f(t, u) $, we found a minimal and a maximal positive solution by the method of sequence approximation. Moreover, based on the properties of Green's function and fixed point index theorem, the existence of multiple positive solutions for a singular $ p $-Laplacian fractional differential equation with infinite-point boundary conditions was obtained and, at last, an example was given to demonstrate the validity of our main results.

Keywords

• hadamard fractional differential equation
• multiple positive solutions
• infinite-point
• minimal and maximal positive solutions