Series method to solve conformable fractional ric-cati differential equations
DOI:
https://doi.org/10.14419/ijamr.v6i1.7238Published:
2017-02-26Keywords:
Conformable Fractional Derivative, Conformable Fractional Integral, Power Series, Riccati Equation, Series Solution.Abstract
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] 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).
License
Authors who publish with this journal agree to the following terms:
                          [1]           Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
                          [2]           Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
                          [3]           Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).