Geodesic
Implicit hybrid methods for solving fractional Riccati equation
Syam, Muhammed I. 1 ; Alsuwaidi, Azza 1 ; Alneyadi, Asia 1 ; Al Refai, Safa 1 ; Al Khaldi, Sondos 1
1 Department of Mathematical Sciences, United Arab Emirates University, UAE
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 2, p. 124-134.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we modify the implicit hybrid methods for solving fractional Riccati equation. Similar methods are implemented for the ordinary derivative and we are the first who implement it for fractional derivative case. This approach is of higher order comparing with the existing methods in the literature. We study the convergence, zero stability, consistency, and region of absolute stability. Numerical results are presented to show the efficiency of the proposed method.
DOI : 10.22436/jnsa.012.02.06
Classification : 35C08, 74J35
Keywords: Fractional Riccati equation, implicit hybrid methods, convergence

Syam, Muhammed I.  1 ; Alsuwaidi, Azza  1 ; Alneyadi, Asia  1 ; Al Refai, Safa  1 ; Al Khaldi, Sondos  1

1 Department of Mathematical Sciences, United Arab Emirates University, UAE 
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     title = {Implicit hybrid methods for solving fractional {Riccati} equation},
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Syam, Muhammed I. ; Alsuwaidi, Azza ; Alneyadi, Asia ; Al Refai, Safa ; Al Khaldi, Sondos . Implicit hybrid methods for solving fractional Riccati equation. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 2, p. 124-134. doi : 10.22436/jnsa.012.02.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.02.06/

[1] Al-Mdallal, Q. M.; Syam, M. I.; M. N. Anwar A collocation-shooting method for solving fractional boundary value problems , Commun. Nonlinear Sci. Numer. Simul., Volume 15 (2010), pp. 3814-3822 | Zbl | DOI

[2] Aminikhah, H.; Sheikhani, A. H. R.; Rezazadeha, H. Approximate analytical solutions of distributed order fractional Riccati differential equation, Ain Shams Eng. J., Volume 2016 (2016), pp. 1-8 | DOI

[3] S. Balaji Legendre wavelet operational matrix method for solution of fractional order Riccati differential equation, J. Egyptian Math. Soc., Volume 23 (2015), pp. 263-270 | DOI | Zbl

[4] Bota, C.; B. Caruntu Analytical approximate solutions for quadratic Riccati differential equation of fractional order using the Polynomial Least Squares Method, Chaos Solitons Fractals, Volume 102 (2017), pp. 339-345 | DOI | Zbl

[5] El-Sayed, M. F.; Syam, M. I. Electrohydrodynamic instability of a dielectric compressible liquid sheet streaming into an ambient stationary compressible gas, Arc. Appl. Mech., Volume 77 (2007), pp. 613-626 | Zbl

[6] El-Sayed, M. F.; Syam, M. I. Numerical study for the electrified instability of viscoelastic cylindrical dielectric fluid film surrounded by a conducting gas, Phy. A: Stat. Mech. Appl., Volume 377 (2007), pp. 381-400 | DOI

[7] Ghomanjani, F. A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations, J. Egyptian Math. Soc., Volume 24 (2016), pp. 638-643 | Zbl | DOI

[8] Hamarsheh, M.; Ismail, A. I.; Odibat, Z. An Analytic Solution for Fractional Order Riccati Equations by Using Optimal Homotopy Asymptotic Method, Volume 10 (2016), pp. 1131-1150

[9] Jafari, H.; H. Tajadodi He’s Variational Iteration Method for Solving Fractional Riccati Differential Equation , Int. J. Differ. Equ., Volume 2010 (2010), pp. 1-8 | Zbl

[10] M. M. Khader Numerical treatment for solving fractional Riccati differential equation, J. Egyptian Math. Soc., Volume 21 (2013), pp. 32-37 | Zbl | DOI

[11] Khalil, R.; Horani, M. Al; Yousef, A.; Sababheh, M. A new definition of fractional derivative, J. Comput. Appl. Math., Volume 264 (2014), pp. 65-70 | DOI

[12] Khan, N. A.; Ara, A.; N. A. Khan Fractional-order Riccati differential equation: Analytical approximation and numerical results, Adv. Difference Equ., Volume 2013 (2013), pp. 1-16 | Zbl | DOI

[13] Khana, N. A.; Ara, A.; Jamil, M. An efficient approach for solving the Riccati equation with fractional orders, Comput. Math. Appl., Volume 61 (2011), pp. 2683-2689 | Zbl | DOI

[14] Lambert, J. D. Numerical Methods for Ordinary Differential Systems , John Wiley & Sons, Chichester, 1991

[15] Y. L. Li Solving a nonlinear fractional differential equation using Chebyshev wavelets, Commun. Nonlinear Sci. Numer. Simul., Volume 15 (2010), pp. 2284-2292 | DOI | Zbl

[16] Li, X. Y.; Wu, B. Y.; Wang, R. T. Reproducing kernel method for fractional Riccati differential equations, Abstr. Appl. Anal., Volume 2014 (2014), pp. 1-6

[17] Lu, Bin Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations, Phys. Lett. A, Volume 376 (2012), pp. 2045-2048 | DOI | Zbl

[18] Momani, S.; N. Shawagfeh Decomposition method for solving fractional Riccati differential equations , Appl. Math. Comput., Volume 182 (2006), pp. 1083-1092 | DOI | Zbl

[19] Odibat, Z.; Momani, S. Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order, Chaos Solitons Fractals, Volume 36 (2008), pp. 167-174 | Zbl | DOI

[20] Raja, M. Z.; Manzar, M.; Samarc, R. An efficient computational intelligence approach for solving fractional order Riccati equations using ANN and SQP, Appl. Math. Model., Volume 39 (2015), pp. 3075-3093 | DOI

[21] M. G. Sakar; Akgül, A.; D. Baleanu On solutions of fractional Riccati differential equations, Adv. Difference Equ., Volume 2017 (2017), pp. 1-10 | DOI

[22] Syam, M. I. Cubic spline interpolation predictors over implicitly defined curves, J. Comput. Appl. Math., Volume 157 (2003), pp. 283-295 | DOI | Zbl

[23] Syam, M. I. The modified Broyden-variational method for solving nonlinear elliptic differential equations, Chaos Solitions Fractals, Volume 32 (2007), pp. 392-404 | DOI | Zbl

[24] Syam, M. I.; B. S. Attili Numerical solution of singularly perturbed fifth order two point boundary value problem, Appl. Math. Comput., Volume 170 (2005), pp. 1085-1094 | DOI | Zbl

[25] Syam, M. I.; Siyyam, H. I. An efficient technique for finding the eigenvalues of fourth-order Sturm-Liouville problems, Chaos Solitons Fractals, Volume 39 (2009), pp. 659-665 | Zbl | DOI

[26] Syam, M. I.; Siyyam, H. I. Numerical differentiation of implicitly defined curves, J. Comput. Appl. Math., Volume 108 (1999), pp. 131-144 | DOI

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