## Tbilisi Mathematical Journal

- Tbilisi Math. J.
- Volume 8, Issue 2 (2015), 23-33.

### A perspective on fractional Laplace transforms and fractional generalized Hankel-Clifford transformation

#### Abstract

In this study a relation between the Laplace transform and the generalized Hankel-Clifford transform is established. The relation between distributional generalized Hankel-Clifford transform and distributional one sided Laplace transform is developed. The results are verified by giving illustrations. The relation between fractional Laplace and fractional generalized Hankel-Clifford transformation is also established. Further inversion theorem considering fractional Laplace and fractional generalized Hankel-Clifford transformation is proved in Zemanian space.

#### Article information

**Source**

Tbilisi Math. J., Volume 8, Issue 2 (2015), 23-33.

**Dates**

Received: 7 August 2014

Accepted: 22 September 2014

First available in Project Euclid: 12 June 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.tbilisi/1528769003

**Digital Object Identifier**

doi:10.1515/tmj-2015-0004

**Mathematical Reviews number (MathSciNet)**

MR3323917

**Zentralblatt MATH identifier**

1309.26009

**Subjects**

Primary: 26A3

Secondary: 44A10: Laplace transform 44A20: Transforms of special functions 46F12: Integral transforms in distribution spaces [See also 42-XX, 44-XX]

**Keywords**

Generalized Hankel-Clifford transforms Laplace Transforms generalized Hankel-Clifford inversion theorem testing function space for generalized Hankel-Clifford transform and Laplace transforms fractional Laplace transforms and fractional generalized Hankel-Clifford transformation

#### Citation

Gorty, V. R. Lakshmi. A perspective on fractional Laplace transforms and fractional generalized Hankel-Clifford transformation. Tbilisi Math. J. 8 (2015), no. 2, 23--33. doi:10.1515/tmj-2015-0004. https://projecteuclid.org/euclid.tbilisi/1528769003