Martinez, Francisco and Kaabar, Mohammed K. A. (2024) Martínez-Kaabar Fractal-Fractional Laplace Transformation with Applications to Integral Equations. Symmetry-Basel, 16 (11). p. 1483. ISSN 2073-8994, DOI https://doi.org/10.3390/sym16111483.
Full text not available from this repository.Abstract
This paper addresses the extension of Martinez-Kaabar (MK) fractal-fractional calculus (for simplicity, in this research work, it is referred to as MK calculus) to the field of integral transformations, with applications to some solutions to integral equations. A new notion of Laplace transformation, named MK Laplace transformation, is proposed, which incorporates the MK alpha,gamma-integral operator into classical Laplace transformation. Laplace transformation is very applicable in mathematical physics problems, especially symmetrical problems in physics, which are frequently seen in quantum mechanics. Symmetrical systems and properties can be helpful in applications of Laplace transformations, which can help in providing an effective computational tool for solving such problems. The main properties and results of this transformation are discussed. In addition, the MK Laplace transformation method is constructed and applied to the non-integer-order first- and second-kind Volterra integral equations, which exhibit a fractal effect. Finally, the MK Abel integral equation's solution is also investigated via this technique.
| Item Type: | Article |
|---|---|
| Funders: | UNSPECIFIED |
| Uncontrolled Keywords: | fractal-fractional integral equations; fractal-fractional differentiation and integration; fractal-fractional Laplace transformation |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms. Juhaida Abd Rahim |
| Date Deposited: | 18 Feb 2025 03:30 |
| Last Modified: | 18 Feb 2025 03:30 |
| URI: | http://eprints.um.edu.my/id/eprint/47371 |
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