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

<p>In this paper, we introduce a generalized Mellin transformation in a general form that encompasses the generalized Mellin transformations found in the literature. Then, we give the fundamental properties of this new integral transformation and apply it to some elementary functions. Furthermore, we obtain the solutions of partial and fractional differential equations by means of this new integral transformation. Finally, we examine the relations between generalized Mellin transformations in the literature and the new generalized Mellin transformation and present a table showing the new integral transformations of functions commonly used in mathematics, physics and engineering applications.</p>
</abstract>

In this paper, we introduce a generalized Mellin transformation in a general form that encompasses the generalized Mellin transformations found in the literature. Then, we give the fundamental properties of this new integral transformation and apply it to some elementary functions. Furthermore, we obtain the solutions of partial and fractional differential equations by means of this new integral transformation. Finally, we examine the relations between generalized Mellin transformations in the literature and the new generalized Mellin transformation and present a table showing the new integral transformations of functions commonly used in mathematics, physics and engineering applications.

New generalized Mellin transform and applications to partial and fractional differential equations

International Journal of Mathematics and Computer in Engineering

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

In this paper, we introduce a generalized Mellin transformation in a general form that encompasses the generalized Mellin transformations found in the...

New generalized Mellin transform and applications to partial and fractional differential equations

Published Online: Jun 09, 2023

Page range: 45 - 66

Received: Mar 31, 2023

Accepted: May 17, 2023

DOI: https://doi.org/10.2478/ijmce-2023-0004

Keywords
Mellin transform, partial differential equations, fractional differential equations, fractional derivatives and integrals

© 2023 Enes Ata et al., published by Sciendo

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

New generalized Mellin transform and applications to partial and fractional differential equations

Published Online: Jun 09, 2023

Page range: 45 - 66

Received: Mar 31, 2023

Accepted: May 17, 2023

DOI: https://doi.org/10.2478/ijmce-2023-0004

KeywordsMellin transform, partial differential equations, fractional differential equations, fractional derivatives and integrals

© 2023 Enes Ata et al., published by Sciendo

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

Keywords
Mellin transform, partial differential equations, fractional differential equations, fractional derivatives and integrals