MIXED PROBLEM FOR THE FRACTIONAL ORDER WAVE PROPAGATION EQUATION
Article Sidebar
Main Article Content
Abstract
This article investigates a mixed boundary value problem for the fractional-order wave propagation equation. Differential equations involving fractional derivatives provide a more accurate description of complex dynamic processes compared to classical wave equations. The mathematical model of the fractional-order wave equation is presented and its physical interpretation is discussed. Based on the given initial and boundary conditions, the existence and uniqueness of the solution to the mixed problem are analyzed. Analytical and numerical solution methods are compared and discussed, and several examples are provided to verify the obtained results. The findings of the study contribute to a deeper understanding of physical processes governed by fractional differential equations and offer a theoretical foundation for their practical modeling. This problem was solved using Fourier's method, one of the most common methods in mathematical physics.
Downloads
Article Details
Section
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain the copyright of their manuscripts, and all Open Access articles are disseminated under the terms of the Creative Commons Attribution License 4.0 (CC-BY), which licenses unrestricted use, distribution, and reproduction in any medium, provided that the original work is appropriately cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations.
How to Cite
References
1.Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, Elsevier (2006).
2.R. Ashurov, Yu. Fayziev, “On the nolocal boundary value problems for time- fractional equations,” Fractal and Fractional, 6, 41 (2022).
3.A.V.Pskhu The Stankovich Integral transform and Its Applications, Special Functions and Analysis of Differntial Equations, 2020, p.16.
4.Umarov S., Hahn M., Kobayashi K. Beyond the triangle: Browian motion, Ito calculas, and Fokker-Plank equation-fractional generalizations. World Scientifi. 2017.