The arbitrary-order fractional hyperbolic nonlinear scalar conservation law

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

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Official URL: https://doi.org/10.1186/s13662-020-02697-8

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
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

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