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The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann-Liouville Derivative

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  • Dumitru Baleanu
  • Mohsen Alipour
  • Hossein Jafari

Abstract

We obtain the approximate analytical solution for the fractional quadratic Riccati differential equation with the Riemann-Liouville derivative by using the Bernstein polynomials (BPs) operational matrices. In this method, we use the operational matrix for fractional integration in the Riemann-Liouville sense. Then by using this matrix and operational matrix of product, we reduce the problem to a system of algebraic equations that can be solved easily. The efficiency and accuracy of the proposed method are illustrated by several examples.

Suggested Citation

  • Dumitru Baleanu & Mohsen Alipour & Hossein Jafari, 2013. "The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann-Liouville Derivative," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, June.
    • Handle: RePEc:hin:jnlaaa:461970
    DOI: 10.1155/2013/461970
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    Cited by:

    1. Ahmad Sami Bataineh & Osman Rasit Isik & Moa’ath Oqielat & Ishak Hashim, 2021. "An Enhanced Adaptive Bernstein Collocation Method for Solving Systems of ODEs," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    2. Bakhshandeh-Chamazkoti, Rohollah & Alipour, Mohsen, 2022. "Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 97-107.

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