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 c D ^α u ( t ) − a^ c D^ 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.