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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

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

  • [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.
Year 2017, Volume: 5 Issue: 1, 193 - 200, 03.04.2017

Abstract

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 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.
There are 19 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

A. Ebadıan

F. Farahrooz This is me

A. A. Khajehnasırı This is me

Publication Date April 3, 2017
Submission Date April 3, 2017
Acceptance Date January 20, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

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. April 2017;5(1):193-200.
Chicago Ebadıan, A., F. Farahrooz, and A. A. Khajehnasırı. “HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM”. Konuralp Journal of Mathematics 5, no. 1 (April 2017): 193-200.
EndNote Ebadıan A, Farahrooz F, Khajehnasırı AA (April 1, 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, and A. A. Khajehnasırı, “HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM”, Konuralp J. Math., vol. 5, no. 1, pp. 193–200, 2017.
ISNAD Ebadıan, A. et al. “HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM”. Konuralp Journal of Mathematics 5/1 (April 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. et al. “HOMOTOPY ANALYSIS METHOD FOR THE SOLUTION OF FUZZY FRACTIONAL TELEGRAPH EQUATION BY USING LAPLACE TRANSFORM”. Konuralp Journal of Mathematics, vol. 5, no. 1, 2017, pp. 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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