Positive solutions for a system of nonlocal fractional boundary value problems

Abstract

We investigate the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations, subject to multipoint boundary conditions. Existence results for systems of nonlinear Hammerstein integral equations are also presented. Some nontrivial examples are included.MSC 2010 : Primary 34A08; Secondary 45G15

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

“…Fractional BVPs defined on intervals have been studied by many authors. Many results on the existence, uniqueness, multiplicity, and nonexistence of solutions for fractional differential equations subject to various boundary conditions (BCs) have been obtained; see for example [1,2,4,7,8,11,12,13,14,15,16,17,19,20,25,26,27]. To the best of our knowledge, no work has been done for fractional BVPs on graphs.…”

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

“…With this advantage, fractional-order models have become more realistic and practical than the corresponding classical integer-order models. For some recent development on the topic, see [1], [2], [4], [5], [6], [7], [8], [9], [10], [11], [12], [14], [17], and the references therein. The study of coupled systems of fractional order differential equations is also very significant as such systems appear in a variety of problems of applied nature, especially in biosciences.…”

Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations

“…For some recent work on the topic, see [1,4,6,11,16,19,28,30,31,37]. Specially, the study of coupled systems of fractional order differential equations has been addressed extensively by several researchers, see [3,5,18,20,21,29,33,36,40] and the references cited therein. For instance, By applying some standard fixed point theorems, Jiang et al [23] and Yuan et al [41] considered the existence of positive solutions to the four-point coupled boundary value problems for systems of nonlinear semipositone fractional differential equations under different conditions, respectively.…”