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A Novel Formulation of the Fractional Derivative with the Order α ≥ 0 and without the Singular Kernel

Author

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  • Hassan Kamil Jassim

    (Department of Mathematics, University of Thi-Qar, Nasiriyah 64001, Iraq)

  • Mohammed A. Hussein

    (Scientific Research Center, Thi Qar University, Thi-Qar 64001, Iraq
    Scientific Research Center, Al-Ayen University, Thi-Qar 64001, Iraq)

Abstract

A new definition of fractional derivative (NFD) with order α ≥ 0 , is developed in this paper. The new derivative has a smooth kernel that takes on two different representations for the temporal and spatial variables. The advantage of the proposed approach over traditional local theories and fractional models with a singular kernel lies in the possibility that there is a class of problems capable of describing scale-dependent fluctuations and material heterogeneities. Moreover, it has been shown that the NFD converges to the classical derivative faster than some other fractional derivatives.

Suggested Citation

  • Hassan Kamil Jassim & Mohammed A. Hussein, 2022. "A Novel Formulation of the Fractional Derivative with the Order α ≥ 0 and without the Singular Kernel," Mathematics, MDPI, vol. 10(21), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4123-:d:963782
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    References listed on IDEAS

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    1. Hossein Jafari & Hassan Kamil Jassim & Dumitru Baleanu & Yu-Ming Chu, 2021. "On The Approximate Solutions For A System Of Coupled Korteweg–De Vries Equations With Local Fractional Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-7, August.
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    Cited by:

    1. Hassan Kamil Jassim & Mohammed Abdulshareef Hussein, 2023. "A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations," Mathematics, MDPI, vol. 11(7), pages 1-13, March.

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