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HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM

Yıl 2017, Cilt: 5 Sayı: 1, 193 - 200, 03.04.2017

Öz

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.

Kaynakça

  • [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 modi ed 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 di erential 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 di erential 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 modi ed 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 Di erential for fuzzy function, J. Math. Anal. Appl. 91 (1983) 552-558.
Yıl 2017, Cilt: 5 Sayı: 1, 193 - 200, 03.04.2017

Öz

Kaynakça

  • [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 modi ed 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 di erential 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 di erential 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 modi ed 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 Di erential for fuzzy function, J. Math. Anal. Appl. 91 (1983) 552-558.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Articles
Yazarlar

A. Ebadıan

F. Farahrooz Bu kişi benim

A. A. Khajehnasırı Bu kişi benim

Yayımlanma Tarihi 3 Nisan 2017
Gönderilme Tarihi 3 Nisan 2017
Kabul Tarihi 20 Ocak 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 1

Kaynak Göster

APA Ebadıan, A., Farahrooz, F., & Khajehnasırı, A. A. (2017). HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM. Konuralp Journal of Mathematics, 5(1), 193-200.
AMA Ebadıan A, Farahrooz F, Khajehnasırı AA. HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM. Konuralp J. Math. Nisan 2017;5(1):193-200.
Chicago Ebadıan, A., F. Farahrooz, ve A. A. Khajehnasırı. “HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM”. Konuralp Journal of Mathematics 5, sy. 1 (Nisan 2017): 193-200.
EndNote Ebadıan A, Farahrooz F, Khajehnasırı AA (01 Nisan 2017) HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM. Konuralp Journal of Mathematics 5 1 193–200.
IEEE A. Ebadıan, F. Farahrooz, ve A. A. Khajehnasırı, “HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM”, Konuralp J. Math., c. 5, sy. 1, ss. 193–200, 2017.
ISNAD Ebadıan, A. vd. “HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM”. Konuralp Journal of Mathematics 5/1 (Nisan 2017), 193-200.
JAMA Ebadıan A, Farahrooz F, Khajehnasırı AA. HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM. Konuralp J. Math. 2017;5:193–200.
MLA Ebadıan, A. vd. “HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM”. Konuralp Journal of Mathematics, c. 5, sy. 1, 2017, ss. 193-00.
Vancouver Ebadıan A, Farahrooz F, Khajehnasırı AA. HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM. Konuralp J. Math. 2017;5(1):193-200.
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