Resonant Integral Boundary Value Problems for Caputo Fractional Differential Equations

Abstract

This paper deals with the following Caputo fractional differential equations with Riemann-Stieltjes integral boundary conditions Dc0+αut=ft,ut,u′t,u′′t,  t∈0,1,  u0=u′′0=0,  u1=∫01‍utdAt, where Dc0+α denotes the standard Caputo derivative, α∈(2,3]; ∫01x(t)dA(t) denotes the Riemann-Stieltjes integrals of x with respect to A. By mean of coincidence degree theory, we obtain the existence of solutions for the above fractional BVP at resonance. In the end, according to the main results, we give a typical example.