The arbitrary-order fractional hyperbolic nonlinear scalar conservation law
Document Type
Article
Publication Date
1-1-2020
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).
Keywords
Jumarie’s modification of Riemann–Liouville, Variable-order calculus, Variable-order fractional characteristic method, Variable-order fractional scalar conservation law
Divisions
MathematicalSciences
Funders
University Malaya grant GF033-2018
Publication Title
Advances in Difference Equations
Volume
2020
Issue
1
Publisher
SpringerOpen