摘要：In this paper, we concerned the existence of solutions of the following nonlinear mixed fractional differential equation with the integral boundary value problem:$$\left \{ \textstyle\begin{array}{l} {}^{C}D^{\alpha}_{1-} D^{\beta}_{0+}u(t)=f(t,u(t),D^{\beta +1}_{0+}u(t),D^{\beta}_{0+}u(t)),\quad 0< t< 1,\\ u(0)=u'(0)=0,\qquad u(1)=\int^{1}_{0}u(t)\,dA(t), \end{array}\displaystyle \right . $$ where ${}^{C}D^{\alpha}_{1-}$ is the left Caputo fractional derivative of order $\alpha\in(1,2]$, and $D^{\beta}_{0+}$ is the right Riemann–Liouville fractional derivative of order $\beta\in(0,1]$. The coincidence degree theory is the main theoretical basis to prove the existence of solutions of such problems..
关键词：Left Caputo fractional derivative ; Right Riemann–Liouville fractional derivative ; Boundary value problem ; Resonance ; Coincidence degree theory ;
