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Approximation of sequential fractional systems of Liouville–Caputo type by discrete delta difference operators

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  • Almusawa, Musawa Yahya
  • Mohammed, Pshtiwan Othman

Abstract

We present the Liouville–Caputo fractional difference method for the numerical evolution of the sequential differential equation of fractional order. Meanwhile, some binomial coefficients are considered in discrete fractional calculus to find and determine the corresponding sequence of continuous fractional order equations. Finally, a standard numerical test is offered in detail to demonstrate the validity of the main theorem.

Suggested Citation

  • Almusawa, Musawa Yahya & Mohammed, Pshtiwan Othman, 2023. "Approximation of sequential fractional systems of Liouville–Caputo type by discrete delta difference operators," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923009992
    DOI: 10.1016/j.chaos.2023.114098
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    References listed on IDEAS

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    1. Thabet Abdeljawad, 2013. "On Delta and Nabla Caputo Fractional Differences and Dual Identities," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, July.
    2. Pshtiwan Othman Mohammed & Thabet Abdeljawad & Faraidun Kadir Hamasalh, 2021. "On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis," Mathematics, MDPI, vol. 9(11), pages 1-17, June.
    3. Abdeljawad, Thabet & Baleanu, Dumitru, 2017. "Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 106-110.
    4. Pshtiwan Othman Mohammed & Dumitru Baleanu & Eman Al-Sarairah & Thabet Abdeljawad & Nejmeddine Chorfi, 2023. "Theoretical And Numerical Computations Of Convexity Analysis For Fractional Differences Using Lower Boundedness," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(08), pages 1-12.
    5. Mohammed, Pshtiwan Othman & Kürt, Cemaliye & Abdeljawad, Thabet, 2022. "Bivariate discrete Mittag-Leffler functions with associated discrete fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
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