Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation - Moustafa El-Shahed (Abstract and Applied Analysis)
We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: D0+αu(t)+λa(t) f(u(t))=0, 0<t<1, u(0)=u′(0)=u′(1)=0, where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.