Download This PaperFractional Derivatives of Some Fractional Functions and Their Applications
Asian Journal of Applied Science and Technology (AJAST), (Quarterly International Journal) Volume 4, Issue 1, Pages 147-158, January-March 2020
12 Pages Posted: 5 May 2020
Date Written: 2020
Abstract
In this paper, we make use of the fractional differential operator method to find the modified Riemann-Liouville (R-L) fractional derivatives of some fractional functions include fractional polynomial function, fractional exponential function, fractional sine and cosine functions. The Mittag-Leffler function plays an important role in our article, and the fractional differential operator method can be applied to find the particular solutions of non-homogeneous linear fractional differential equations (FDE) with constant coefficients in a unified way and it is a generalization of the method of finding particular solutions of classical ordinary differential equations. On the other hand, several examples are illustrative for demonstrating the advantage of our approach and we compare our results with the traditional differential calculus cases.
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