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A Müntz wavelets collocation method for solving fractional differential equations

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Abstract

In this paper, we introduce a new set of wavelets, namely Müntz wavelets. These wavelets are defined based on Müntz Legendre polynomials which have the property of orthogonality. We stabilize the wavelet coefficients by utilizing Jacobi polynomials to construct the modified Müntz wavelets. Next, we present a collocation scheme based on Müntz wavelets for solving fractional differential equations. The fractional derivative is described in the Caputo sense. Some error estimates are given and numerical examples are included to demonstrate the applicability and accuracy of the proposed method. This includes the elastic-dissipative mathematical model of linear mechanical devices known as Boltzman operator.

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Authors and Affiliations

  1. Department of Mathematics, Isfahan (Khorasgan) branch, Islamic Azad University, Isfahan, Iran

    M. Bahmanpour, Majid Tavassoli-Kajani & M. Maleki

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  1. M. Bahmanpour
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  2. Majid Tavassoli-Kajani
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  3. M. Maleki
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Correspondence to Majid Tavassoli-Kajani.

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Communicated by José Tenreiro Machado.

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Bahmanpour, M., Tavassoli-Kajani, M. & Maleki, M. A Müntz wavelets collocation method for solving fractional differential equations. Comp. Appl. Math. 37, 5514–5526 (2018). https://doi.org/10.1007/s40314-018-0636-0

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  • DOI: https://doi.org/10.1007/s40314-018-0636-0

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