Theory and Applications of the Triple Laplace Transform for Local Derivative with the Mittag Leffler Kernel
Abstract
This article aims to provide a practical and reliable approach to solving fractional M-derivative partial differential equations with nine parameters that involve the Mittag-Leffler function. Several theorems have been developed to describe and express the M-derivative triple Laplace transform. Furthermore, these defined concepts and theorems are demonstrated by applying them to fractional partial differential equations. This proposed transformation appears to efficiently enable finding solutions to partial differential equations with M-derivatives that match mathematical, engineering, and physical models.
Keywords
References
- Abdeljawad, T., (2015), On conformable fractional calulus, J. Comput. Appl. Math., 279, 57-66.
- AK Thakur and S Panda. (2015) Some properties of triple Laplace transform. Int. J. Math. Comput. Sci. 2, 23-8.
- Atangana A., (2013) A Note on the Triple Laplace Transform and Its Applications to Some Kind of Third-Order Differential Equation. Hindawi Publishing Corporation Abstract and Applied Analysis. Article ID 769102, 10 pages.http://dx.doi.org/10.1155/2013/769102.
- Bas, E., Acay, B., and T. Abdeljawad (2020) Non-local fractional calculus from different viewpoint generated by truncated M-derivative Journal of Computational and Applied Mathematics 366 112410.
- Jarad, F., Abdeljawad, T., (2020) Generalized fractional derivatives and Laplace transform, American Institute of Mathematical Sciences, Volume 13, Issue 3: 709-722. Doi: 10.3934/dcdss.2020039.
- J.V.D.C Sousa, E.C. de Oliviera, (2017) A New Truncated M-fractional derivative type unifying some fractional derivative types with classical properties.,arXiv:1704.08187.
- Katugampola, U.N. (2011) A new approach to generalized fractional derivatives. arXiv:1106.0965.
- Khalil, R., Horani, M. Al., Yousef, A., Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65-70.
Details
Primary Language
English
Subjects
Applied Mathematics (Other)
Journal Section
Research Article
Publication Date
April 11, 2026
Submission Date
June 23, 2025
Acceptance Date
October 17, 2025
Published in Issue
Year 2026 Volume: 10 Number: 1
APA
Baş, E., & Özküçük, B. (2026). Theory and Applications of the Triple Laplace Transform for Local Derivative with the Mittag Leffler Kernel. Journal of Innovative Science and Engineering, 10(1), 18-36. https://doi.org/10.38088/jise.1725770
AMA
1.Baş E, Özküçük B. Theory and Applications of the Triple Laplace Transform for Local Derivative with the Mittag Leffler Kernel. JISE. 2026;10(1):18-36. doi:10.38088/jise.1725770
Chicago
Baş, Erdal, and Burak Özküçük. 2026. “Theory and Applications of the Triple Laplace Transform for Local Derivative With the Mittag Leffler Kernel”. Journal of Innovative Science and Engineering 10 (1): 18-36. https://doi.org/10.38088/jise.1725770.
EndNote
Baş E, Özküçük B (April 1, 2026) Theory and Applications of the Triple Laplace Transform for Local Derivative with the Mittag Leffler Kernel. Journal of Innovative Science and Engineering 10 1 18–36.
IEEE
[1]E. Baş and B. Özküçük, “Theory and Applications of the Triple Laplace Transform for Local Derivative with the Mittag Leffler Kernel”, JISE, vol. 10, no. 1, pp. 18–36, Apr. 2026, doi: 10.38088/jise.1725770.
ISNAD
Baş, Erdal - Özküçük, Burak. “Theory and Applications of the Triple Laplace Transform for Local Derivative With the Mittag Leffler Kernel”. Journal of Innovative Science and Engineering 10/1 (April 1, 2026): 18-36. https://doi.org/10.38088/jise.1725770.
JAMA
1.Baş E, Özküçük B. Theory and Applications of the Triple Laplace Transform for Local Derivative with the Mittag Leffler Kernel. JISE. 2026;10:18–36.
MLA
Baş, Erdal, and Burak Özküçük. “Theory and Applications of the Triple Laplace Transform for Local Derivative With the Mittag Leffler Kernel”. Journal of Innovative Science and Engineering, vol. 10, no. 1, Apr. 2026, pp. 18-36, doi:10.38088/jise.1725770.
Vancouver
1.Erdal Baş, Burak Özküçük. Theory and Applications of the Triple Laplace Transform for Local Derivative with the Mittag Leffler Kernel. JISE. 2026 Apr. 1;10(1):18-36. doi:10.38088/jise.1725770
