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Editorial: Overview and Some New Directions

Author

Listed:
  • GUO-CHENG WU

    (Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China)

  • THABET ABDELJAWAD

    (Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia)

  • FERHAN ATICI

    (Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101-3576, USA)

  • CARLOS LIZAMA

    (Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile)

Abstract

The fractional derivative holds historical dependence or memory effects. But it also brings error accumulation of the numerical solutions as well as the theoretical analysis since many properties from the integer order case cannot hold. The fractional difference is discrete counterpart of the fractional derivative. The memory kernel is defined by applying the discrete functions on time scale and avoids the errors from the numerical discretization. It is particularly suitable for fractional modeling with computer implementations. Many applications of fractional dynamics to neural networks, signal processing, time series and big data become possible now. This issue of work presents the latest progress in the neighborhood related to fractional calculus.

Suggested Citation

  • Guo-Cheng Wu & Thabet Abdeljawad & Ferhan Atici & Carlos Lizama, 2021. "Editorial: Overview and Some New Directions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-6, December.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:08:n:s0218348x21020035
    DOI: 10.1142/S0218348X21020035
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