Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

Abstract

We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.

Existence of Positive Solutions for a System of Singular Fractional Boundary Value Problems with p-Laplacian Operators

“…By (19), (20) and the absolute continuity of the integral function, we deduce that A 1 (S) is equicontinuous. By a similar approach, we obtain that A 2 (S) is also equicontinuous, and so A(S) is equicontinuous.…”

On a singular Riemann–Liouville fractional boundary value problem with parameters

“…For some recent results on the existence, nonexistence and multiplicity of positive solutions for fractional differential equations and systems of fractional differential equations with various boundary conditions, we refer the reader to the monographs [10,36] and the papers [2,3,8,12,13,17,19,25,28,30,31,34]. We also mention the books [14,15,24,26,27] and the papers [5-7, 21-23, 29] for applications of the fractional differential equations in various disciplines.…”

Positive solutions for a system of fractional differential equations with p-Laplacian operator and multi-point boundary conditions

“…. , 4, given by (10), (11), (16), and (17), we refer the reader to [7,Lemma 2.3]. We present now some properties of the Green functions G 1 and G 2 that will be used in the next sections.…”