Series method to solve conformable fractional ric-cati differential equations

  • Authors

    • Mohammed Al Masalmeh Higher colleges of technology
    2017-02-26
    https://doi.org/10.14419/ijamr.v6i1.7238
  • Conformable Fractional Derivative, Conformable Fractional Integral, Power Series, Riccati Equation, Series Solution.
  • This paper investigates and states some properties of conformable fractional derivative, Further Study and applies the series solution for a case of conformable fractional Riccati deferential equation with variable coefficients “which is arising in stochastic games†or “hyperbolic boundary control." Recently, Prof. Roshdi Khalil introduced a new and interesting definition for the C F D, which is simpler than the previous definition in Caputo and Riemann-Liouville. It leads to many extensions of the classical theorems in calculus.

  • References

    1. [1] K.Assaleh; W. M.Ahmed, Modeling of speech signals using fractional calculus 9th international symposium on Signal Processing and its Applications, 2007.ISSPA 2007.12-15 Feb. 2007 Page: 1-4.

      [2] R. Khalil, M. A. Horani, A. Youssef and M. Sababheh, A new definition of fractional derivative, J. Compute. Appl. Math. 264, 65-70 (2104).

      [3] Abdeljawad, Thabet, on conformable fractional calculus, J. Computational. Applied. Math. 279(2015) 57-66. https://doi.org/10.1016/j.cam.2014.10.016.

      [4] A. El-Ajou, O. Abu Arqub, Z. Al Zhour and S. Momani, New Results on Fractional Power Series: Theories and Applications, Entropy 2013, 15, 5305-5323; https://doi.org/10.3390/e15125305.

      [5] K.S. Miller, An introduction to fractional calculus and Fractional differential Equations, J. Wiley and Sons, New York, 1993.

      [6] Bagley RL, Torvik PJ. A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol 1983; 27(3):201-10. https://doi.org/10.1122/1.549724.

      [7] Hartley TT, Lorenzo CF, Qammar HK. Chaos in a fractional order Chua system. IEEE Trans. Circ. Syst. I1995; 42(8):485-90.

      [8] Magin RL. Fractional calculus in bioengineering. Crit. Rev. Biomed Eng. 2004; 32(1):1-104. https://doi.org/10.1615/CritRevBiomedEng.v32.10.

      [9] K. Busawon, P. Johnson, Solution of a class of Riccati Equations, WSEAS International Conference on Applied Mathematics, Tenerife, Spain, Dec 16-18,2005(pp334-338).

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  • How to Cite

    Al Masalmeh, M. (2017). Series method to solve conformable fractional ric-cati differential equations. International Journal of Applied Mathematical Research, 6(1), 30-33. https://doi.org/10.14419/ijamr.v6i1.7238