Positive solutions for fractional boundary value problems under a generalized fractional operator

Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems

This paper is devoted to the existence of multiple positive solutions for fractional boundary value problem DC0+αu(t)=f(t, u(t), u'(t)), 0<t<1, u(1)=u'(1)=u''(0)=0, where 2<α≤3 is a real number, DC0+α is the Caputo fractional derivative, and f:[0,1]×[0, +∞)×R→[0, +∞) is continuous. Firstly, by constructing a special cone, applying Guo-Krasnoselskii's fixed point theorem and Leggett-Williams fix...

Positive Solutions for Systems of Coupled Fractional Boundary Value Problems

We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions which contain some positive constants.

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Positive solutions to a class of q-fractional difference boundary value problems with φ-Laplacian operator

By virtue of the upper and lower solutions method, as well as the Schauder fixed point theorem, the existence of positive solutions to a class of q-fractional difference boundary value problems with φ-Laplacian operator is investigated. The conclusions here extend existing results. c ©2016 All rights reserved.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation