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An efficient Haar wavelet collocation method for the numerical solution of multi-term fractional differential equations

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Abstract

In the numerical analysis, Wavelets play an important role in the solution of differential equations. In this paper, we apply the Haar wavelet collocation method (HWCM) for solving multi-term fractional differential equations (FDEs) using the fractional order operational matrix of integration. The present study is illustrated by exploring different kinds of FDEs that gives the approximate solution is good agreement with the exact solution than the Haar wavelet-based method presented by Li and Zhao (Appl Math Comput 216:2276–2285, 2010) and other methods by Ford and Connolly (J Comput Appl Math 229:382–391, 2009), El-Sayed et al. (Appl Math Comput 60:788–797, 2010). The error will be reduced by increasing the number of collocation points, which has been justified through the examples.

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Acknowledgments

We are thankful to the anonymous reviewers for their valuable suggestions. The authors acknowledge the financial support of UGC’s Research Fellowship in Science for Meritorious Students (RFSMS) vide sanction letter no. F. 4-1/2006(BSR)/7-101/2007(BSR), dated-02/01/2013.

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  1. P. G. Department of Studies in Mathematics, Karnatak University, Dharwad, 580003, Karnataka, India

    S. C. Shiralashetti & A. B. Deshi

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  1. S. C. Shiralashetti
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  2. A. B. Deshi
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Correspondence to S. C. Shiralashetti.

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Shiralashetti, S.C., Deshi, A.B. An efficient Haar wavelet collocation method for the numerical solution of multi-term fractional differential equations. Nonlinear Dyn 83, 293–303 (2016). https://doi.org/10.1007/s11071-015-2326-4

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  • DOI: https://doi.org/10.1007/s11071-015-2326-4

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