New Results on Fractional Power Series: Theories and Applications

被引：168

作者：

El-Ajou, Ahmad ^{[1
]}

Abu Arqub, Omar ^{[1
]}

Al Zhour, Zeyad ^{[2
]}

Momani, Shaher ^{[3
]}

机构：

[1] Al Balqa Appl Univ, Fac Sci, Dept Math, Salt 19117, Jordan

[2] Univ Dammam, Coll Engn, Dept Basic Sci & Humanities, Dammam 31451, Saudi Arabia

[3] Univ Jordan, Fac Sci, Dept Math, Amman 11942, Jordan

来源：

ENTROPY | 2013年 / 15卷 / 12期

关键词：

Fractional power series; Caputo fractional derivative; Fractional differential equations; DIFFERENTIAL-EQUATIONS; ENTROPY; DIFFUSION; DERIVATIVES; TSALLIS;

D O I：

10.3390/e15125305

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

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.

引用

页码：5305 / 5323

页数：19

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