{"references": ["[1]\tV. E. Tarasov, Mathematical economics: application of fractional calculus, Mathematics, vol. 8, no. 5, 660, 2020.", "[2]\tMohd. Farman Ali, Manoj Sharma, Renu Jain, An application of fractional calculus in electrical engineering, Advanced Engineering Technology and Application, vol. 5, no. 2, pp, 41-45, 2016.", "[3]\tJ. T. Machado, Fractional Calculus: Application in Modeling and Control, Springer New York, 2013.", "[4]\tF. Mainardi, Fractional calculus: some basic problems in continuum and statistical mechanics, Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, Eds., pp. 291-348, Springer, Wien, Germany, 1997.", "[5]\tR. Magin, Fractional calculus in bioengineering, part 1, Critical Reviews in Biomedical Engineering, vol. 32, no,1. pp.1-104, 2004.", "[6]\tA. Dzielinski, D. Sierociuk, Ultracapacitor modelling and control using discrete fractional order state-space model, Acta Montanistica Slovaca, vol. 13, no. 1, pp. 136-145, 2008.", "[7]\tC. Cattani, H. M. Srivastava, and X. -J. Yang, (Eds.), Fractional Dynamics, Emerging Science Publishers (De Gruyter Open), Berlin and Warsaw, 2015.", "[8]\tC. -H. Yu, A study on fractional RLC circuit, International Research Journal of Engineering and Technology, vol. 7, no. 8, pp. 3422-3425, 2020.", "[9]\tC. -H. Yu, Study on fractional Newton's law of cooling, International Journal of Mechanical and Industrial Technology, vol. 9, no. 1, pp. 1-6, 2021.", "[10]\tC. -H. Yu, A new insight into fractional logistic equation, International Journal of Engineering Research and Reviews, vol. 9, no. 2, pp.13-17, 2021,"]}

Abstract: This paper studies the fractional differential problems of two types of fractional analytic functions based on Jumarie’s modified Riemann-Liouville (R-L) fractional derivative. Any order fractional derivatives of these two types of fractional analytic functions can be obtained by using fractional Euler’s formula, fractional DeMoivre’s formula, and fractional Fourier series method. A new multiplication of fractional analytic functions plays an important role in this paper. In fact, our results are generalizations of the results of classical calculus. On the other hand, two examples are provided to illustrate our results. Keywords: fractional differential problems, fractional analytic functions, Jumarie’s modified R-L fractional derivative, fractional Euler’s formula, fractional DeMoivre’s formula, fractional Fourier series, new multiplication. Title: A Study of Some Fractional Differential Problems Author: Chii-Huei Yu International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Vol. 10, Issue 1, April 2022 - September 2022 Page No: 52-58 Research Publish Journals Website: www.researchpublish.com Published Date: 09-September-2022 DOI: https://doi.org/10.5281/zenodo.7064096 Paper Download Link (Source) https://www.researchpublish.com/papers/a-study-of-some-fractional-differential-problems

International Journal of Mathematics and Physical Sciences Research, ISSN 2348-5736 (Online), Research Publish Journals, Website: www.researchpublish.com