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Upper and lower solutions method and a fractional differential equation boundary value problem. (English) Zbl 1183.34009

Summary: The method of lower and upper solutions for the fractional differential equation

D δ u(t)+g(t,u(t))=0,t(0,1),1<δ2,

with Dirichlet boundary condition

u(0)=a,u(1)=b

is used to give sufficient conditions for the existence of at least one solution.

MSC:
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
34A45Theoretical approximation of solutions of ODE
47N20Applications of operator theory to differential and integral equations