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Hadamard Fractional Calculus On Time Scales

Author

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  • TING-TING SONG

    (School of Mathematical Sciences, Bohai University, Jinzhou 121013, P. R. China2Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China)

  • GUO-CHENG WU

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

  • JIA-LI WEI

    (School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, Jiangsu Province, P. R. China)

Abstract

This study defines a Hadamard fractional sum by use of the time-scale theory. Then a h-fractional difference is given and fundamental theorems are proved. Initial value problems of fractional difference equations are presented and their equivalent fractional sum equations are provided. The discrete Mittag-Leffler function solutions of linear fractional difference equations are obtained. It can be concluded that the new discrete fractional calculus of Hadamard type is well defined.

Suggested Citation

  • Ting-Ting Song & Guo-Cheng Wu & Jia-Li Wei, 2022. "Hadamard Fractional Calculus On Time Scales," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-14, November.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x22501456
    DOI: 10.1142/S0218348X22501456
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    Cited by:

    1. He, Jin-Man & Pei, Li-Jun, 2023. "Function matrix projection synchronization for the multi-time delayed fractional order memristor-based neural networks with parameter uncertainty," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    2. Li, Xin & Ma, Weiyuan & Bao, Xionggai, 2024. "Generalized fractional calculus on time scales based on the generalized Laplace transform," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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