# Series solutions of systems of nonlinear fractional differential equations

Research output: Contribution to journalArticle

26 Citations (Scopus)

### 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 189-198 10 Acta Applicandae Mathematicae 105 2 https://doi.org/10.1007/s10440-008-9271-x Published - Feb 2009

### Fingerprint

Homotopy Analysis Method
Series Solution
Fractional Differential Equation
Nonlinear Differential Equations
Differential equations
Fractional Order
Chemistry
Physics
Differential equation
Engineering
Decomposition

### Keywords

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

### ASJC Scopus subject areas

• Applied Mathematics

### Cite this

In: Acta Applicandae Mathematicae, Vol. 105, No. 2, 02.2009, p. 189-198.

Research output: Contribution to journalArticle

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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.

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