Open AccessAnalysis of a derivative with two variable orders
Author(s) -
Abdon Atangana,
AUTHOR_ID,
Ali Akgül,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022406
Subject(s) - derivative (finance) , kernel (algebra) , variable (mathematics) , mathematics , fractal , exponential function , dimension (graph theory) , fractional calculus , fractal dimension , order (exchange) , fractal derivative , mathematical analysis , pure mathematics , fractal analysis , finance , financial economics , economics
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.