Existence for boundary value problems of two-term Caputo fractional differential equations

This paper is concerned with a class of boundary value problem of nonlinear fractional differential equation \(^cD^α u(t)-a^cD^β u(t)+f(t,u(t))=0\). This equation may be regarded as an extension of Bagley-Torvik equations. Some new existence and uniqueness results are obtained by using standard Banach contraction principle and Krasnoselskii’s fixed point theorem.