1. New definitions of fractional derivatives and integrals for complex analytic functions.
- Author
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Abu-Ghuwaleh, Mohammad and Saadeh, Rania
- Subjects
FRACTIONAL calculus ,ANALYTIC functions ,MATHEMATICAL functions ,CAPUTO fractional derivatives ,SPECIAL functions ,ZETA functions ,DEFINITIONS - 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]
- Published
- 2023
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