Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales by Svetlin G. Georgiev

Author:Svetlin G. Georgiev
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

such that

and

Note that such time scales exist. For instance,

and

Suppose that z is a complex number such that

(2.12)

The solution of the problem

satisfies

Note that the products for n = m are understood to be 1. Thus, using Definition 2.2, we make the following definition.

Definition 2.7

If is a function, then the Laplace transform is defined by

for all satisfying (2.12) for which the series converges.

We define

Theorem 2.14

For all , we have

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