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An Efficient Method for Solving Systems of Linear Ordinary and Fractional Differential Equations

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Abstract

This paper presents a reliable approach for solving linear systems of ordinary and fractional differential equations. First, the FDEs or ODEs of a system with initial conditions to be solved are transformed to Volterra integral equations. Then Taylor expansion for the unknown function and integration method are employed to reduce the resulting integral equations to a new system of linear equations for the unknown and its derivatives. The fractional derivatives are considered in the Riemann–Liouville sense. Some numerical illustrations are given to demonstrate the effectiveness of the proposed method in this paper.

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Authors and Affiliations

  1. Department of Mathematics, Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran

    Mohsen Didgar

  2. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Nafiseh Ahmadi

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  1. Mohsen Didgar
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  2. Nafiseh Ahmadi
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Correspondence to Mohsen Didgar.

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Communicated by Mohsen Didgar.

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Didgar, M., Ahmadi, N. An Efficient Method for Solving Systems of Linear Ordinary and Fractional Differential Equations. Bull. Malays. Math. Sci. Soc. 38, 1723–1740 (2015). https://doi.org/10.1007/s40840-014-0060-6

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  • DOI: https://doi.org/10.1007/s40840-014-0060-6

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