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Khibiev, A., Alikhanov, A. and Huang, C. (2023) A Second-Order Difference Scheme for Generalized Time-Fractional Diffusion Equation with Smooth Solutions. Computational Methods in Applied Mathematics, 24, 101-117.
https://doi.org/10.1515/cmam-2022-0089

has been cited by the following article:

• TITLE: A Hybrid ESA-CCD Method for Variable-Order Time-Fractional Diffusion Equations

  AUTHORS: Xiaoxue Lu, Chunhua Zhang, Huiling Xue, Bowen Zhong

  KEYWORDS: Variable-Order Caputo Fractional Derivative, Combined Compact Difference Method, Exponential-Sum-Approximation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.9, September 10, 2024

  ABSTRACT: In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential-sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixth-order hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments.