Numerical Solutions of Fractional Differential Equations by Using Fractional Taylor Basis |
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| Vidhya Saraswathy Krishnasamy, Somayeh Mashayekhi and Mohsen Razzaghi, "Numerical Solutions of Fractional Differential Equations by Using Fractional Taylor Basis," IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 98-106, Jan. 2017. |
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| Authors: | Vidhya Saraswathy Krishnasamy Somayeh Mashayekhi Mohsen Razzaghi |
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| Affiliation: | 1. Department of Mathematics and Statistics, Mississippi State University, MS 39762, USA;2. Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA |
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| Abstract: | In this paper, a new numerical method for solving fractional differential equations (FDEs) is presented. The method is based upon the fractional Taylor basis approximations. The operational matrix of the fractional integration for the fractional Taylor basis is introduced. This matrix is then utilized to reduce the solution of the fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of this technique. |
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| Keywords: | Caputo derivative fractional differential equations (FEDs) fractional Taylor basis operational matrix Riemann-Liouville fractional integral operator |
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