Title

Exponential Functions and Laplace Transforms for Alpha Derivatives

Abstract

We introduce the exponential function for alpha derivatives on generalized time scales. We also define the Laplace transform that helps to solve higher order linear alpha dynamic equations on generalized time scales. If ® = ¾, the Hilger forward jump operator, then our theory contains the theory of delta dynamic equations on time scales as a special case. If ® = ½, the Hilger backward jump operator, then our theory contains the theory of nabla dynamic equations on time scales as a special case. Hence differential equations, difference equations (using the forward or backward difference operator), or q-difference equations (using the forward or backward q-difference operator) can be accommodated within our theory. We also present various properties of the Laplace transform and offer some examples.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Alpha derivative; Exponential function; Generalized time scale; Laplace Transform

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2004 CRC Press, All rights reserved.

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