TITLE:
Finite Volume Element Method for Fractional Order Neutral Time-Delay Differential Equations
AUTHORS:
Zicheng Wei, Qing Yang
KEYWORDS:
Fractional Order Time-Delay Differential Equation, Finite Volume Element Method, L1 Approximation, Error Estimation, Numerical Simulation
JOURNAL NAME:
Engineering,
Vol.17 No.1,
January
20,
2025
ABSTRACT: Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control systems, signal processing, etc. Therefore, it is of great significance to study fractional-order time-delay differential equations. In this paper, we discuss a finite volume element method for a class of fractional-order neutral time-delay differential equations. By introducing an intermediate variable, the fourth-order problem is transformed into a system of equations consisting of two second-order partial differential equations. The L1 formula is used to approximate the time fractional order derivative terms, and the finite volume element method is used in space. A fully discrete format of the equations is established, and we prove the existence, uniqueness, convergence and stability of the solution. Finally, the validity of the format is verified by numerical examples.