Positive solutions to boundary value problems of p-Laplacian with fractional derivative

Abstract

In this article, we consider the following boundary value problem of nonlinear fractional differential equation with p-Laplacian operator:continuous. One of the difficulties here is that the corresponding Green's function G(t, s) is singular at s = 0. By the use of an approximation method and fixed point theorems on cone, some existence and multiplicity results of positive solutions are acquired. Some examples are presented to illustrate the main results.

The method of lower and upper solutions for the general boundary value problems of fractional differential equations with p-Laplacian

“…For studying this kind of problems, the models of the p-Laplacian equation are introduced, see [17]. Many important results for the boundary value problems of fractional p-Laplacian equations have been obtained, see [18][19][20][21][22][23][24][25][26][27][28] and the references therein.…”

Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p-Laplacian operator

“…It is quite natural to study fractional differential equation relative to equation (1.2). Recently, many scholars have paid more attention to the fractional order differential equation boundary value problems with p-Laplacian operator, see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In [15], Lu .…”

Positive Solutions of Fractional Differential Equations with p-Laplacian

“…Liu et al [13], Dong et al [8], and Zhang et al [25] studied -Laplacian boundary value problems with fractional derivative. By using the fixedpoint index theory, they obtained the existence of positive solutions.…”

“…On the other hand, because of the wide mathematical and physical background, the existence of positive solutions for nonlinear integer-order boundary values problems with -Laplacian operator has received wide attention (see [8,12,13,21,[24][25][26][27][28][29]). For example, Su et al [28] considered the following four-point boundary values problems withLaplacian operator:…”