<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

Publié en ligne: 09 juin 2023

Pages: 45 - 66

Reçu: 31 mars 2023

Accepté: 17 mai 2023

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

Mots clés
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

Publié en ligne: 09 juin 2023

Pages: 45 - 66

Reçu: 31 mars 2023

Accepté: 17 mai 2023

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

Mots clésMellin 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.

Mots clés
Mellin transform, partial differential equations, fractional differential equations, fractional derivatives and integrals