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

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 o...

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Bibliographic Details
Published in:International Journal of Mathematics and Computer in Engineering 2023-06, Vol.1 (1), p.45-66
Main Authors: Ata, Enes, Onur Kıymaz, I.
Format: Article
Language:English
Subjects:
26A33
34A08
35A08
44A05
fractional derivatives and integrals
fractional differential equations
Mellin transform
partial differential equations
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Summary: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.
ISSN:2956-7068
2956-7068
DOI:10.2478/ijmce-2023-0004