Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales

الملخص EN

The definition of Caputo fractional derivative is given and some of its properties are discussed in detail.

After then, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Caputo nabladerivative are studied.

Also the explicit solutions to homogeneous equations and nonhomogeneous equations are derived by using Laplace transform method.