Existence of Integral and Anti-periodic Boundary Valued Problem of Fractional Order 0<α≤3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<\alpha \le 3$$\end{document}

We are concerned with the existence of solutions of a class of fractional differential equations with anti-periodic and integral boundary conditions involving the Caputo fractional derivative with order α∈(0,3]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (0,3]$$\end{document}. We give three results based on Banach fixed-point theorem, and Schauder fixed-point theorems.