Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator

Abstract EN

We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation with p-Laplacian operator D0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0, 01, (ϕp)-1=ϕq, 1/p+1/q=1.

By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained.

Finally, an example is given to show the effectiveness of our works.