A New Generalized Definition of Fractal–Fractional Derivative with Some Applications

Autor:	Francisco Martínez, Mohammed K. A. Kaabar
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	fractal–fractional differentiation fractal–fractional integration fractal–fractional derivative in Caputo sense fractal–fractional ordinary differential equations Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939 Electronic computers. Computer science QA75.5-76.95
Zdroj:	Mathematical and Computational Applications, Vol 29, Iss 3, p 31 (2024)
Druh dokumentu:	article
ISSN:	2297-8747 1300-686X
DOI:	10.3390/mca29030031
Popis:	In this study, a new generalized fractal–fractional (FF) derivative is proposed. By applying this definition to some elementary functions, we show its compatibility with the results of the FF derivative in the Caputo sense with the power law. The main elements of classical differential calculus are introduced in terms of this new derivative. Thus, we establish and demonstrate the basic operations with derivatives, chain rule, mean value theorems with their immediate applications and inverse function’s derivative. We complete the theory of generalized FF calculus by proposing a notion of integration and presenting two important results of integral calculus: the fundamental theorem and Barrow’s rule. Finally, we analytically solve interesting FF ordinary differential equations by applying our proposed definition.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/93bdd84652a74b17bede93cdf61fb3c9 Zobrazit plný text záznamu View record in DOAJ