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On the Stability of Linear Incommensurate Fractional-Order Difference Systems

Author

Listed:
  • Noureddine Djenina

    (Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Laarbi Tebessi, Tebessa 12002, Algeria)

  • Adel Ouannas

    (Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Laarbi Tebessi, Tebessa 12002, Algeria)

  • Iqbal M. Batiha

    (Department of Mathematics, University of Jordan, Amman 11942, Jordan)

  • Giuseppe Grassi

    (Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy)

  • Viet-Thanh Pham

    (Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam)

Abstract

To follow up on the progress made on exploring the stability investigation of linear commensurate Fractional-order Difference Systems (FoDSs), such topic of its extended version that appears with incommensurate orders is discussed and examined in this work. Some simple applicable conditions for judging the stability of these systems are reported as novel results. These results are formulated by converting the linear incommensurate FoDS into another equivalent system consists of fractional-order difference equations of Volterra convolution-type as well as by using some properties of the Z -transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems.

Suggested Citation

  • Noureddine Djenina & Adel Ouannas & Iqbal M. Batiha & Giuseppe Grassi & Viet-Thanh Pham, 2020. "On the Stability of Linear Incommensurate Fractional-Order Difference Systems," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1754-:d:426827
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    References listed on IDEAS

    as
    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    2. Fahd Jarad & Kenan Taş, 2012. "On Sumudu Transform Method in Discrete Fractional Calculus," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, September.
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    1. Noureddine Djenina & Adel Ouannas & Iqbal M. Batiha & Giuseppe Grassi & Taki-Eddine Oussaeif & Shaher Momani, 2022. "A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior," Mathematics, MDPI, vol. 10(13), pages 1-16, June.

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