Singular Positone and Semipositone Boundary Value Problems of Nonlinear Fractional Differential Equations

Abstract

We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problemD0+αu(t)=μa(t)f(t,u(t)), 0<t<1,u(0)=u(1)=u′(0)=u′(1)=0, whereμ>0,a,andfare continuous,α∈(3,4]is a real number, andD0+αis Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to illustrate the main results.