Solutions of a fractional oscillator by using differential transform method

Adel Al-rabtah; Vedat Suat Ertürk; Shaher Momani

doi:10.1016/j.camwa.2009.06.036

Solutions of a fractional oscillator by using differential transform method

Adel Al-rabtah
, Vedat Suat Ertürk
, Shaher Momani

University of Mutah
Ondokuz Mayis University

Research output: Contribution to journal › Article › peer-review

81 Scopus citations

Abstract

In this paper, we present an efficient algorithm for solving a fractional oscillator using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of a fractional oscillator. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.

Original language	English
Pages (from-to)	1356-1362
Number of pages	7
Journal	Computers and Mathematics with Applications
Volume	59
Issue number	3
DOIs	https://doi.org/10.1016/j.camwa.2009.06.036
State	Published - Feb 2010
Externally published	Yes

Keywords

Caputo fractional derivative
Differential transform method
Fractional differential equation
Fractional oscillator
Numerical solutions

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10.1016/j.camwa.2009.06.036

Cite this

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abstract = "In this paper, we present an efficient algorithm for solving a fractional oscillator using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of a fractional oscillator. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.",

keywords = "Caputo fractional derivative, Differential transform method, Fractional differential equation, Fractional oscillator, Numerical solutions",

author = "Adel Al-rabtah and Ert{\"u}rk, \{Vedat Suat\} and Shaher Momani",

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AU - Ertürk, Vedat Suat

AU - Momani, Shaher

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N2 - In this paper, we present an efficient algorithm for solving a fractional oscillator using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of a fractional oscillator. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.

AB - In this paper, we present an efficient algorithm for solving a fractional oscillator using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of a fractional oscillator. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.

KW - Caputo fractional derivative

KW - Differential transform method

KW - Fractional differential equation

KW - Fractional oscillator

KW - Numerical solutions

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SP - 1356

EP - 1362

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 3

ER -

Solutions of a fractional oscillator by using differential transform method

Abstract

Keywords

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