Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions

Abstract

The authors study a type of nonlinear fractional boundary value problem with non-homogeneous integral boundary conditions. The existence and uniqueness of positive solutions are discussed. An example is given as the application of the results.MSC 2010 : 34B15, 34B18, 34A08, 26A33

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.…”

Unique positive solution for a fractional boundary value problem

“…Recently, there are many papers dealing with the existence of solutions (or positive solutions) of nonlinear initial or boundary value problems for fractional differential equations by virtue of techniques of nonlinear analysis (fixed-point theorems, Leray-Schauder theory, lower and upper solution method, etc. ), for example, see [1,2,5,6,10,15,16,17] and the references therein.…”