文章基本信息

标题：The arbitrary-order fractional hyperbolic nonlinear scalar conservation law
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作者：S. M. Reza Shirkhorshidi ; D. Rostamy ; W. A. M. Othman 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-27
DOI：10.1186/s13662-020-02697-8
出版社：Hindawi Publishing Corporation
摘要：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.
关键词：Variable-order calculus;Variable-order fractional characteristic method;Variable-order fractional scalar conservation law;Jumarie’s modification of Riemann–Liouville;