Hendy, A.S. and De Staelen, R.H. (2020) Theoretical Analysis (Convergence and Stability) of a Difference Approximation for Multiterm Time Fractional Convection Diffusion-Wave Equations with Delay. Mathematics, 8, Article No. 1696.
https://doi.org/10.3390/math8101696

has been cited by the following article:

• 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.