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New Ultraspherical Wavelets Spectral Solutions for Fractional Riccati Differential Equations

Author

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  • W. M. Abd-Elhameed
  • Y. H. Youssri

Abstract

We introduce two new spectral wavelets algorithms for solving linear and nonlinear fractional-order Riccati differential equation. The suggested algorithms are basically based on employing the ultraspherical wavelets together with the tau and collocation spectral methods. The main idea for obtaining spectral numerical solutions depends on converting the differential equation with its initial condition into a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. For the sake of illustrating the efficiency and the applicability of our algorithms, some numerical examples including comparisons with some algorithms in the literature are presented.

Suggested Citation

  • W. M. Abd-Elhameed & Y. H. Youssri, 2014. "New Ultraspherical Wavelets Spectral Solutions for Fractional Riccati Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, May.
    • Handle: RePEc:hin:jnlaaa:626275
    DOI: 10.1155/2014/626275
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    Cited by:

    1. Waseem, Waseem & Sulaiman, M. & Aljohani, Abdulah Jeza, 2020. "Investigation of fractional models of damping material by a neuroevolutionary approach," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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