Existence and uniqueness of solutions for fractional boundary value problems with p-Laplacian operator

Abstract

In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem involving the p-Laplacian operator. Our analysis relies on some properties of the Green function and the Guo-Krasnoselskii fixed point theorem and the Banach contraction mapping principle. Two examples are given to illustrate our theoretical results. MSC: 26A33; 34A08; 76F70

Existence–uniqueness and monotone iteration of positive solutions to nonlinear tempered fractional differential equation with p-Laplacian operator

“…Especially, fractional differential equations have been proved to be powerful tools in the modeling of various phenomena in various fields of science and engineering, for example fluid mechanics, physics and heat conduction; see for instance [1][2][3][4][5][6]. Meanwhile, it is well known that the p-Laplacian operator is also used in analyzing biology, physics, mechanics and the related fields of mathematical modeling; see [7][8][9][10][11][12][13][14]. In [7], for studying the turbulent flow in porous media, Leibenson introduced the p-Laplacian differential equation as follows:…”

On stability analysis and existence of positive solutions for a general non-linear fractional differential equations

“…For instance, Khan et al investigated the existence criterion for solutions for FDEs involving the φ p -Laplacian operator in [36]. The EU of results for FDEs with φ p -Laplacian operator are analyzed by Chuanzhi Bai in [37] via fixed point theorems. Also we present the Green function's properties and two examples to illustrate the results.…”

Multiple positive solutions for nonlinear high-order Riemann–Liouville fractional differential equations boundary value problems with p-Laplacian operator

“…In [15], the author is concerned with the existence and uniqueness of positive solutions for the following boundary value problem with p-Laplacian operator:…”