Fractional Differential Equations With ▽ Derivative On Time Scales

This paper mainly studies some results about fractional differential equations withderivative on time scales. Firstly, as preparation,-Laplace transform, fractional-power function,-Mittag-Leffler function on time scales are discussed. Then we define fractional-integrals and fractional Riemann-Liouville-derivatives and Caputo-derivatives on time scales and discuss their properties. The existence of the solution and the dependency of the solution upon the initial value on Cauchy type problem with Riemann-Liouville-derivatives and Caputo-derivatives are presented. In addition, using Laplace transform method, we show the solution to fractional differential equations with Riemann-Liouville-derivative on time scales.Finally, sequential linear differential equations of fractional order on time scales are studied, and the general solution structure are presented.