Series solutions of systems of nonlinear fractional differential equations

A. S. Bataineh; A. K. Alomari; M. S.M. Noorani; I. Hashim; R. Nazar

doi:10.1007/s10440-008-9271-x

Series solutions of systems of nonlinear fractional differential equations

A. S. Bataineh
, A. K. Alomari
, M. S.M. Noorani
, I. Hashim
, R. Nazar

Universiti Kebangsaan Malaysia

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

34 Scopus citations

Abstract

Differential equations of fractional order appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method (ADM) solution as special cases.

Original language	English
Pages (from-to)	189-198
Number of pages	10
Journal	Acta Applicandae Mathematicae
Volume	105
Issue number	2
DOIs	https://doi.org/10.1007/s10440-008-9271-x
State	Published - Feb 2009
Externally published	Yes

Keywords

Caputo fractional derivative
Homotopy analysis method
System of nonlinear fractional differential equations

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10.1007/s10440-008-9271-x

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title = "Series solutions of systems of nonlinear fractional differential equations",

abstract = "Differential equations of fractional order appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method (ADM) solution as special cases.",

keywords = "Caputo fractional derivative, Homotopy analysis method, System of nonlinear fractional differential equations",

author = "Bataineh, \{A. S.\} and Alomari, \{A. K.\} and Noorani, \{M. S.M.\} and I. Hashim and R. Nazar",

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T1 - Series solutions of systems of nonlinear fractional differential equations

AU - Bataineh, A. S.

AU - Alomari, A. K.

AU - Noorani, M. S.M.

AU - Hashim, I.

AU - Nazar, R.

PY - 2009/2

Y1 - 2009/2

N2 - Differential equations of fractional order appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method (ADM) solution as special cases.

AB - Differential equations of fractional order appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method (ADM) solution as special cases.

KW - Caputo fractional derivative

KW - Homotopy analysis method

KW - System of nonlinear fractional differential equations

UR - https://www.scopus.com/pages/publications/58149490845

U2 - 10.1007/s10440-008-9271-x

DO - 10.1007/s10440-008-9271-x

M3 - Article

AN - SCOPUS:58149490845

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SP - 189

EP - 198

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 2

ER -

Series solutions of systems of nonlinear fractional differential equations

Abstract

Keywords

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