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| Title: | Exponential functions and laplace transforms for alpha derivatives |
| Author (s): | Akin, Elvan Bohner, Martin |
| Department/Lab Affiliations: | Mathematics & Statistics |
| Keywords: | Alpha derivative Exponential function Generalized time scale Laplace Transform |
| Issue Date: | 2004 |
| Publisher: | CRC Press |
| Citation: | Akin-Bohner, Elvan, and Bohner, Martin. "Exponential Functions and Laplace Transforms for Alpha Derivatives." Proceedings of the Sixth International Conference on Difference Equations, (2004). |
| 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. |
| Type: | Article - Conference proceedings text |
| Copyright Notice: | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. FULL COPYRIGHT INFORMATION: |
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| title | Exponential functions and laplace transforms for alpha derivatives |
| contributor.author | Akin, Elvan |
| contributor.author | Bohner, Martin |
| contributor.deptlab | Mathematics & Statistics |
| subject | Alpha derivative |
| subject | Exponential function |
| subject | Generalized time scale |
| subject | Laplace Transform |
| date.issued | 2004 |
| publisher | CRC Press |
| identifier.citation | Akin-Bohner, Elvan, and Bohner, Martin. "Exponential Functions and Laplace Transforms for Alpha Derivatives." Proceedings of the Sixth International Conference on Difference Equations, (2004). |
| description.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. |
| type | Article - Conference proceedings |
| type.DCMIType | text |
| type.status | Postprint |
| rights | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. |
| rights.URI | |
| date.accessioned | 2007-04-11T17:00:48Z |
| date.available | 2008-04-21T17:37:06Z |
| identifier.persist.URI |