Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem

Abstract

This article is to study a three-point boundary value problem of Hadamard fractional p-Laplacian differential equation. When our nonlinearity grows ( p − 1 ) -superlinearly and ( p − 1 ) -sublinearly, the existence of positive solutions is obtained via fixed point index. Moreover, using an increasing operator fixed-point theorem, the uniqueness of positive solutions and uniform convergence sequences are also established.

Positive Solutions for a Class of p-Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems

“…Research on Hadamard fractional differential equations is at an early stage; see for example [19][20][21][22][23][24][25][26][27][28][29][30]. In [19], B. Ahmad and S. K. Ntouyas used fixed point theory to study the existence and uniqueness of solutions for a Hadamard type fractional differential equation involving integral boundary conditions…”

“…where f satisfies the Lipschitz condition. On the other hand, p-Laplacian equations are extensively used in physics, mechanics, dynamical systems, etc (see [15][16][17][18][20][21][22][23]31]). For example, Leibenson [31] introduced p-Laplacian differential equations to study a mechanics problem involving turbulent flow in a porous medium.…”

Positive Solutions for a Weakly Singular Hadamard-Type Fractional Differential Equation with Changing-Sign Nonlinearity

“…In particular, the Hadamard derivative is a nonlocal fractional derivative with singular logarithmic kernel. So the study of Hadamard fractional differential equations is relatively difficult; see [26][27][28][29][30][31][32].…”

Solutions for a Singular Hadamard-Type Fractional Differential Equation by the Spectral Construct Analysis

“…In recent years, to enrich the theory of fractional calculus, the fractional derivative and integral were extended to many different forms such as Hadamard, Erdelyi-Kober, Hilfer derivatives, and integrals. In particular, it is more difficult to obtain the qualitative properties of solutions for Hadamard-type fractional differential equations since Hadamard derivatives possess a singular logarithmic kernel [99][100][101][102][103][104][105][106].…”