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New definitions of fractional derivatives and integrals for complex analytic functions.
- Source :
- Arab Journal of Basic & Applied Sciences; Dec2023, Vol. 30 Issue 1, p675-690, 16p
- Publication Year :
- 2023
-
Abstract
- In this paper, we introduce a ground-breaking approach to defining fractional calculus for a selected class of analytic functions. Our new definitions, based on a novel and intuitive understanding of fractional derivatives and integrals, offer improved mathematical tractability for a variety of applications, including physics, engineering and finance. Our approach significantly simplifies the complexity of mathematical functions compared to the traditional Riemann-Liouville approach, by using simple functions rather than special functions, while preserving the intrinsic sense of fractional calculus. This article not only presents our proposed definitions but also provides a thorough analysis of their properties and advantages. The conclusion of this paper discusses the potential for future research in the field of fractional calculus. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 25765299
- Volume :
- 30
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Arab Journal of Basic & Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 174339881
- Full Text :
- https://doi.org/10.1080/25765299.2023.2281064