Shirkhorshidi, Seyed Mohammad Reza and Rostamy, Davood and Othman, Wan Ainun Mior and Awang, Md Abu Omar (2020) The arbitrary-order fractional hyperbolic nonlinear scalar conservation law. Advances in Difference Equations, 2020 (1). p. 253. ISSN 1687-1839, DOI https://doi.org/10.1186/s13662-020-02697-8.
Full text not available from this repository.Abstract
In this paper, we use a new powerful technique of arbitrary-order fractional (AOF) characteristic method (CM) to solve the AOF hyperbolic nonlinear scalar conservation law (HNSCL) of time and space. We present the existence and uniqueness of this class of equations in time and one-dimensional space of fractional arbitrary order. We extend Jumarie’s modification of Riemann–Liouville and Caputo’s definition of the fractional arbitrary order to introduce some formulae (Appl. Math. Lett. 22:378–385, 2009; Appl. Math. Lett. 18:739–748, 2005). Then, we use these formulae to prove the main theorem. In the application section, we use the analytical technique that is presented in the theorem to solve examples that are given. © 2020, The Author(s).
| Item Type: | Article |
|---|---|
| Funders: | University Malaya grant GF033-2018 |
| Uncontrolled Keywords: | Jumarie’s modification of Riemann–Liouville; Variable-order calculus; Variable-order fractional characteristic method; Variable-order fractional scalar conservation law |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms. Juhaida Abd Rahim |
| Date Deposited: | 24 Jun 2020 01:13 |
| Last Modified: | 24 Jun 2020 01:13 |
| URI: | http://eprints.um.edu.my/id/eprint/24952 |
Actions (login required)
 |
View Item |
