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

Author

Listed:
  • 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, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:461970
    DOI: 10.1155/2013/461970
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    References listed on IDEAS

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    5. Mehmet Merdan, 2012. "On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-17, May.
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    Cited by:

    1. A. Jafarian & S. Measoomy Nia & Alireza K. Golmankhaneh & D. Baleanu, 2014. "On Bernstein Polynomials Method to the System of Abel Integral Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Mohsen Alipour & Dumitru Baleanu & Fereshteh Babaei, 2014. "Hybrid Bernstein Block‐Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Ali Ahmadian & Norazak Senu & Farhad Larki & Soheil Salahshour & Mohamed Suleiman & Md. Shabiul Islam, 2013. "Numerical Solution of Fuzzy Fractional Pharmacokinetics Model Arising from Drug Assimilation into the Bloodstream," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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