Existence of Positive Solutions for Boundary Value Problems of Fractional Differential Equations with Parameters
A class of parametric boundary value problems with two-term fractional derivatives and non-zero boundary values is investigated in this paper.Firstly,Green's function is constructed by Laplace transform,and the boundary value problem is transformed into the equivalent second kind of Fredholm integral equation.Secondly,by using the properties of Green's function,Guo-Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem,sufficient conditions for the existence,nonexistence and multiplicity of positive solutions for boundary value problems of fractional differential equations are obtained.Thirdly,the existence of positive solutions for boundary value problems of usual fractional differential equations is extended to boundary value problems with two fractional derivatives.Finally,an example is given to illustrate the feasibility of the obtained results.
two-term fractional derivativesboundary value problemGuo-Krasnoselskii fixed point theoremLeggett-Williams fixed point theoremexistence of positive solutions
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