<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In the present paper a generalization of the Laplace transform is introduced and studied. Its inversion formula is also obtained. As an application, we obtain the generalized fractional Laplace transform of a general class of functions and a product of the Fox’s <italic>H</italic>- function and general class of functions. The results obtained are of general nature and capable of yielding a large number of known or new results as special cases. For illustration, some special cases involving important special functions are mentioned.</p>
</abstract>

In the present paper a generalization of the Laplace transform is introduced and studied. Its inversion formula is also obtained. As an application, we obtain the generalized fractional Laplace transform of a general class of functions and a product of the Fox’s H- function and general class of functions. The results obtained are of general nature and capable of yielding a large number of known or new results as special cases. For illustration, some special cases involving important special functions are mentioned.

On the generalized fractional Laplace transform

Formerly Scientist-B, Defence Research and Development Organization

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On the generalized fractional Laplace transform"}

In the present paper a generalization of the Laplace transform is introduced and studied. Its inversion formula is also obtained. As an application, we obtain...

On the generalized fractional Laplace transform

Published Online: Apr 30, 2021

Page range: 448 - 460

Received: Oct 01, 2020

Accepted: Apr 08, 2021

DOI: https://doi.org/10.2478/mjpaa-2021-0030

Keywords
Laplace transform, -function, Struve’s function, Lommel’s function, Mittag-Leffler functioin, Riemann-zeta function

© 2021 Virendra Kumar, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the generalized fractional Laplace transform

Published Online: Apr 30, 2021

Page range: 448 - 460

Received: Oct 01, 2020

Accepted: Apr 08, 2021

DOI: https://doi.org/10.2478/mjpaa-2021-0030

KeywordsLaplace transform, -function, Struve’s function, Lommel’s function, Mittag-Leffler functioin, Riemann-zeta function

© 2021 Virendra Kumar, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Laplace transform, -function, Struve’s function, Lommel’s function, Mittag-Leffler functioin, Riemann-zeta function