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

Hassan Kamil Jassim () and Mohammed A. Hussein
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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

Mathematics, 2022, vol. 10, issue 21, 1-18

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.

Keywords: new fractional derivative; new fractional integral; integral transforms; existence and uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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