Analysis of a derivative with two variable orders

Abdon Atangana; Ali Akgül; Abdon Atangana; Ali Akgül

doi:10.3934/math.2022406

AIMS Mathematics

2022, Volume 7, Issue 5: 7274-7293. doi: 10.3934/math.2022406

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Research article

Analysis of a derivative with two variable orders

Abdon Atangana ^1,2,
Ali Akgül ^{3
,
,}

1.
Institute for Groundwater Studies, Faculty of Natural and Agricultural Science, University of Free State, 9300, Bloemfontein, South Africa
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
3.
Siirt University, Art and Science Faculty, Department of Mathematics, TR-56100 Siirt, Turkey

Received: 12 August 2021 Revised: 11 January 2022 Accepted: 17 January 2022 Published: 10 February 2022
MSC : 26A33, 33F05

In this paper, we investigate a derivative with the two variable orders. The first one shows the variable order fractal dimension and the second one presents the fractional order. We consider these derivatives with the power law kernel, exponential decay kernel and Mittag-Leffler kernel. We give the theory of this derivative in details. We also present the numerical approximation. The results we obtained in this work are very useful for researchers to improve many things for fractal fractional derivative with two variable orders.
- fractal fractional derivative,
- two variables order,
- theory and applications
Citation: Abdon Atangana, Ali Akgül. Analysis of a derivative with two variable orders[J]. AIMS Mathematics, 2022, 7(5): 7274-7293. doi: 10.3934/math.2022406

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Abstract

In this paper, we investigate a derivative with the two variable orders. The first one shows the variable order fractal dimension and the second one presents the fractional order. We consider these derivatives with the power law kernel, exponential decay kernel and Mittag-Leffler kernel. We give the theory of this derivative in details. We also present the numerical approximation. The results we obtained in this work are very useful for researchers to improve many things for fractal fractional derivative with two variable orders.

References

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