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Abstract: In this paper, we obtain the limit representation of fractional exponential function. The application of fractional exponential function is illustrated. The main methods used in this paper are fractional L’Hospital’s rule, Jumarie’s modified Riemann-Liouville (R-L) fractional derivative, and a new multiplication of fractional analytic functions. In fact, our results are generalizations of the results of classical calculus. Keywords: limit representation, fractional exponential function, fractional L’Hospital’s rule, Jumarie’s modified R-L fractional derivative, new multiplication, fractional analytic functions. Title: Fractional Exponential Function and Its Application 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: 53-57 Research Publish Journals Website: www.researchpublish.com Published Date: 13-September-2022 DOI: https://doi.org/10.5281/zenodo.7074740 Paper Download Link (Source) https://www.researchpublish.com/papers/fractional-exponential-function-and-its-application

International Journal of Mechanical and Industrial Technology, ISSN 2348-7593 (Online), Research Publish Journals, Website: www.researchpublish.com