Convergence analysis of positive solution for Caputo–Hadamard fractional differential equation - Guo, Limin; Li, Cheng; Qiao, Nan; Zhao, Jingbo (Nonlinear Analysis: Modelling and Control, 2025)
By deriving the expression of Green function and some of its special properties and establishing appropriate substitution and appropriate cone, the existence of unique iterative positive, error estimation, and convergence rate of approximate solution are obtained for singular p-Laplacian Caputo–Hadamard fractional differential equation with infinite-point boundary conditions. Nonlinearities involve derivative terms that make our analysis difficult in the course of this research, and we deal with the difficulty of derivative terms by making appropriate substitutions. An example is given to demonstrate the validity of our main results.
Keywords: Caputo–Hadamard fractional differential model; iterative positive solutions; properties of Green’s function; convergence analysis