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A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

Author

Listed:
  • M. Motawi Khashan

    (Department of Basic Sciences, Common First Year, King Saud University, Riyadh 11451, Saudi Arabia)

  • Rohul Amin

    (Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan)

  • Muhammed I. Syam

    (Department of Mathematical Sciences, UAE University, Al-Ain 15551, UAE)

Abstract

In this paper, a new collocation method based on Haar wavelet is developed for numerical solution of Riccati type differential equations with non-integer order. The fractional derivatives are considered in the Caputo sense. The method is applied to one test problem. The maximum absolute estimated error functions are calculated, and the performance of the process is demonstrated by calculating the maximum absolute estimated error functions for a distinct number of nodal points. The results show that the method is applicable and efficient.

Suggested Citation

  • M. Motawi Khashan & Rohul Amin & Muhammed I. Syam, 2019. "A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:545-:d:239955
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    References listed on IDEAS

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    1. 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.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    3. X. Y. Li & B. Y. Wu & R. T. Wang, 2014. "Reproducing Kernel Method for Fractional Riccati Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, April.
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