New Results on Fractional Power Series: Theories and Applications

Entropy

Ahmad El-Ajou¹  Omar Abu Arqub¹  Zeyad Al Zhour² 

[1] Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan; E-Mails:;Department of Basic Sciences and Humanities, College of Engineering, University of Dammam, Dammam 31451, KSA, Saudi Arabia; E-Mail:

关键词: Fractional power series;    Caputo fractional derivative;    Fractional differential equations;   

DOI  :  10.3390/e15125305

来源: mdpi

【 摘 要 】

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. New construction of the generalized Taylor’s power series is obtained. Some applications including approximation of fractional derivatives and integrals of functions and solutions of linear and nonlinear fractional differential equations are also given. In the nonlinear case, the new and simple technique is used to find out the recurrence relation that determines the coefficients of the fractional power series.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.