Existence and Uniqueness of Solutions for the Cauchy-Type Problems of Fractional Differential Equations

Recently, fractional differential equations are applied widely in various fields of science and engineering. Regarding applications of fractional differential equations, we refer to 1– 15 and references cited therein. However, the investigation of basic theory of fractional differential equations is still not complete, and there is a great deal of work which needs to be done. Most of the investigations in this field involve the existence and uniqueness of solutions to fractional differential equations on the finite interval a, b . In 1938, Pitcher and Sewell 16 first considered the nonlinear fractional differential equation