Uniqueness of iterative positive solutions for the singular infinite-point p-Laplacian fractional differential system via sequential technique

Yanqing Feng,Lishan Liu,Limin Guo

doi:10.15388/namc.2020.25.19277

Abstract

By sequential techniques and mixed monotone operator, the uniqueness of positive solution for singular p-Laplacian fractional differential system with infinite-point boundary conditions is obtained. Green's function is derived, and some useful properties of Green' function are obtained. Based on these new properties, the existence of unique positive solutions is established, moreover, an iterative sequence and a convergence rate are given, which are important for practical application, and an example is given to demonstrate the validity of our main results.

Highlights

Boundary value problems for nonlinear fractional differential equations arise from the studies of complex problems in many disciplinary areas such as aerodynamics, fluid flows, electrodynamics of complex medium, electrical networks, rheology, polymer rheology, economics, biology chemical physics, control theory, signal and image processing, blood flow phenomena, and so on
There has been a significant development in the study of fractional differential equations in recent years
Value problems are a significant development for fractional differential equation, and the system in this paper is infinite-points boundary value problem, and about values at infinite-points are involved in the boundary conditions that we refer the reader to [3, 4, 11] and the references therein

Summary

Introduction

Boundary value problems for nonlinear fractional differential equations arise from the studies of complex problems in many disciplinary areas such as aerodynamics, fluid flows, electrodynamics of complex medium, electrical networks, rheology, polymer rheology, economics, biology chemical physics, control theory, signal and image processing, blood flow phenomena, and so on. Value problems are a significant development for fractional differential equation, and the system in this paper is infinite-points boundary value problem, and about values at infinite-points are involved in the boundary conditions that we refer the reader to [3, 4, 11] and the references therein. For p-Laplacian fractional differential equation, we refer the reader to [9, 12]. We consider the following singular infinite-point p-Laplacian nonlinear fractional differential equation system: D0α+ φp D0γ+u (t) + λ1/(q1−1)f t, u(t), D0μ+1 u(t), D0μ+2 u(t), . Compared with [16,17], fractional derivatives are involved in the nonlinear terms, and the solution we obtained is iterative solution, the result is accurate.

Preliminaries and lemmas

Main results

An example