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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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:626275
    DOI: 10.1155/2014/626275
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    References listed on IDEAS

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    1. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second‐Order Differential Equations Involving Singular and Bratu Type Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Odibat, Zaid & Momani, Shaher, 2008. "Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 167-174.
    3. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, October.
    4. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second‐Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second-Order Differential Equations Involving Singular and Bratu Type Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, December.
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    Cited by:

    1. Abdelhamid Rehouma & Hossein Jafari, 2025. "Construction of the Shifted Modified Gegenbauer Polynomials and Approximation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2025(1).

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