Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation

Abstract EN

We consider boundary value problem for nonlinear fractional differential equation D0+αu(t)+f(t,u(t))=0, 03, u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, where D0+α denotes the Caputo fractional derivative.

By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem.

The interesting point lies in the fact that the solutions here are positive, monotone, and concave.