HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM
Year 2017,
Volume: 5 Issue: 1, 193 - 200, 03.04.2017
A. Ebadıan
,
F. Farahrooz
A. A. Khajehnasırı
Abstract
The purpose of this article is to present a numerical method to find an approximate solution for fuzzy fractional differential type equation. This method is applied for linear and non-linear equations and has been examined on two examples. Their solutions compared with the exact solutions. The result show that the proposed method is very simple and e ective.
References
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Year 2017,
Volume: 5 Issue: 1, 193 - 200, 03.04.2017
A. Ebadıan
,
F. Farahrooz
A. A. Khajehnasırı
References
- [1] Eckstein EC, Goldstein JA, Leggas M, The mathematics of suspensions: Kac walks and asymptotic analyticity. Electron J Differ Eqs. 3 (1999) 39-50.
- [2] H.M. Srivastavaa, D. Kumarc, J. Singhc, An effcient analytical technique for fractional model of vibration equation Applied Mathematical Modelling. 45 (2017)192204.
- [3] K. Wang, S. Liu, Application of new iterative transform method and modied fractional homotopy analysis transform method for fractional Fornberg-Whitham equation, J. Nonlinear Sci. Appl. 9 (2016), 2419-2433.
- [4] A.Ebadian, F. Farahrooz, and A. A.Khajehnasiri On the convergence of two-dimensional fuzzy Volterra-Fredholm integral equations by using Picard method , Appl. Appl. Math. 11 (2016), 585- 598.
- [5] Eckstein EC, Leggas M, Ma B, Goldstein JA, Linking theory and measurements of tracer particle position in suspension ows. Proc ASME FEDSM. 251 (2000) 1-8.
- [6] Orsingher E, Beghin L, Time-fractional telegraph equation and telegraph processes with Brownian time. Probab Theory Related Fields, 128 (2004),141-60.
- [7] V. R. Hosseini, W. Chen, Z. Avazzadeh Numerical solution of fractional telegraph equation by using radial basis functions, 38, (2014), 31-39.
- [8] S. Chena, X. Jianga, F. Liub, I. Turnerb, High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation, Journal of Computational and Applied Mathematics. 278 (2015) 119-129.
- [9] T. Allahviranloo, N. Ahmadya, E. Ahmady, Numerical solution of fuzzy differential equations by predictor corrector method. Inf Sci, 177 (2007) 1633-1647.
- [10] Z. Akbarzadeh Ghanaie, M. Mohseni Moghadam, Solving fuzzy dierential equations by Runge-Kutta method. J Math Comput Sci, 2 (2011) 208-221.
- [11] Y. Chalco-Cano, H. Roman-Flores, On new solutions of fuzzy differential equations, Chaos Solitons Fract. 38 (2006) 112-119.
- [12] S. Liang, J. Ma, Laplace transform for the solution of higher order deformation equations arising in the homotopy analysis method,Numer Algor, 67 (2014) 49-57.
- [13] S. Salahshour, T. Allahviranloo, Applications of fuzzy Laplace transforms, Soft Comput 17 (2013) 145-158
- [14] S. Salahshour, T. Allahviranloo Application of fuzzy dierential transform method for solving fuzzy Volterra integral equations, Commun Nonlinear Sci Numer Simulat, 17 (2012) 1372-1381.
- [15] R.C. Mittal , R. Bhatia, A numerical study of two dimensional hyperbolic telegraph equation by modied B-spline differential quadrature method, Applied Mathematics and Computation. 244 (2014), 976-997.
- [16] N. Mikaeilvand, S. Khakrangin Solving fuzzy partial differential equations by fuzzy two dimensional differential transform method, Neural Comput and Applic 60 (2012) 1711-1722.
- [17] A. Salah, M, Khan M. A, Gondal A novel solution procedure for fuzzy fractional heat equations by homotopy analysis transform method, Neural Comput and Applic. 23 (2013) 269-271.
- [18] M.L. Puri, D. Ralescu Fuzzy random variables, J. Math. Anal. Appl. 114 (1986) 409-422.
- [19] M.L. Puri, D. Ralescu Dierential for fuzzy function, J. Math. Anal. Appl. 91 (1983) 552-558.