Positive solutions for a class of nonlinear Hadamard fractional differential equations with a parameter

Abstract

In this paper, we investigate a class of boundary value problem of nonlinear Hadamard fractional differential equations with a parameter. By means of the properties of the Green function and Guo-Krasnosel'skii fixed-point theorem on cones, the existence and nonexistence of positive solutions are obtained. Finally, some examples are presented to show the effectiveness of our main results.

Positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions

“…Hadamard fractional differential equations are also popular in the literature; see [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] and the references therein. In [33], the authors used the Banach contraction principle, the Leray-Schauder's alternative, and Krasnoselskii's fixed-point theorem to study the existence and uniqueness of solutions for the coupled system of nonlinear sequential Caputo and Hadamard fractional differential equations with coupled separated boundary conditions…”

Solutions for a Class of Hadamard Fractional Boundary Value Problems with Sign-Changing Nonlinearity

“…As is known, fractional differential equations have been paid special attention by many researchers for the reason that they serve as an excellent tool for wide applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, and control theory; for more details, we refer to books [1][2][3]. In recent years, there have been a large number of papers dealing with the existence of solutions of nonlinear initial (boundary) value problems of fractional differential equations by using some techniques of nonlinear analysis, such as fixed-point results [4][5][6][7][8][9][10][11][12][13], iterative methods [14][15][16][17][18][19][20][21][22][23], the topological degree [24][25][26][27][28][29], the Leray-Schauder alternative [30,31], and stability [32].…”

Solvability for a class of nonlinear Hadamard fractional differential equations with parameters

“…Although many researchers are paying more and more attention to Hadamard type fractional differential equation, the study of the topic is still in its primary stage. For details and recent developments on Hadamard fractional differential equations, see [41][42][43][44][45][46][47][48].…”