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In this paper, we establish the existence of multiple positive solutions to positone and semipositone Dirichlet-type boundary value problems of the nonlinear fractional differential equation: D0+αu(t)+f(t,u(t))=0,0<t<1,u(0)=u(1)=0 by using the Leray–Schauder nonlinear alternative and a fixed-point theorem on cones, where 1<α<2 is a real number and D0+α is the standard Riemann–Liouville...
In this paper, we consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem D0+αu(t)=f(t,u(t)),0<t<1,u(0)=u(1)=u′(0)=u′(1)=0, where 3<α≤4 is a real number, and D0+α is the standard Riemann–Liouville differentiation. As an application of Green’s function, we give some multiple positive solutions for singular and nonsingular boundary...
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