Abstract: In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional derivative, we study some properties of fractional analytic function, such as fractional Taylor’s theorem, first fractional derivative test, and second fractional derivative test. The major methods used in this paper are fractional Rolle’s theorem, fractional mean value theorem, product rule for fractional derivatives, and a new multiplication of fractional analytic functions. In fact, these new results are generalizations of those results in ordinary calculus.
Keywords: Jumarie’s modified R-L fractional derivative, fractional analytic function, fractional Taylor’s theorem, first and second fractional derivative test, fractional Rolle’s theorem, fractional mean value theorem, product rule for fractional derivatives, new multiplication.
Title: Study on Some Properties of Fractional Analytic Function
Author: Chii-Huei Yu
International Journal of Mechanical and Industrial Technology
ISSN 2348-7593 (Online)
Vol. 10, Issue 1, April 2022 - September 2022
Page No: 31-35
Research Publish Journals
Website: www.researchpublish.com
Published Date: 23-August-2022
