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Analysis of imprecisely defined fuzzy space-fractional telegraph equations

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Abstract

Telegraph equations are very important in physics and engineering due to their importance in modelling and designing frequency or voltage transmission. Moreover, uncertainty present in the system parameters plays a vital role in the designing process. Also it is known that it is not always easy to find exact solution of fractionally ordered system. Taking these factors into consideration, here space-fractional telegraph equations with fuzzy uncertainty have been analysed. A new technique to represent fuzzy number using two different parameters in the same domain has been used along with a semianalytic approach known as Adomain decomposition method (ADM) for the solution. Gaussian and triangular shaped fuzzy numbers are considered to model the uncertainties in initial as well as boundary conditions. The obtained results are compared with the existing solution in special cases for the validation.

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References

  1. J F G Aguilara and D Baleanu, Z. Naturforsch.69, 539 (2014)

    Google Scholar 

  2. A Compte and R Metzler, J. Phys. A30, 7277 (1997)

    ADS  MathSciNet  Google Scholar 

  3. J Chen, F Liu and V Anh, J. Math. Anal. Appl.338, 1364 (2008)

    MathSciNet  Google Scholar 

  4. M Garg, A Sharma and P Manohar, Int. J. Pure Appl. Math.83, 685 (2013)

    Google Scholar 

  5. S Yakubovich and M M Rodrigues, Int. Trans. Spec. Funct.23, 509 (2012)

    Google Scholar 

  6. V H Weston and S He, Inverse Probl. 9, 789 (1993)

    ADS  Google Scholar 

  7. P M Jordan, J. Appl. Phys. 85, 1273 (1999)

    ADS  Google Scholar 

  8. J Banasiak and R Mika, J. Appl. Math. Stoch. Anal. 11, 9 (1998)

    Google Scholar 

  9. J Ford Neville, M Manuela Rodrigues, J Xiao and Y Yan, J. Comp. Appl. Math.249, 95 (2013)

    Google Scholar 

  10. S Momani, Appl. Math. Comp.170, 1126 (2005)

    Google Scholar 

  11. E Orsingher and X Zhao, Chin. Ann. Math.24, 1 (2003)

    Google Scholar 

  12. Z F Ahmad and H Ibrahim, Math. Methods Appl. Sci.36, 1813 (2013)

    MathSciNet  Google Scholar 

  13. Z Zhao and C Li, Appl. Math. Comp.219, 2975 (2012)

    Google Scholar 

  14. Y Khan, J Diblík, N Faraz and Z Šmarda, Adv. Diff. Eqns.2012, 204 (2012)

    Google Scholar 

  15. M Garg, P Manohar and L K Shyam, Int. J. Diff. Eqns.2011, 1 (2011)

    Google Scholar 

  16. A Yıldırım, Int. J. Comput. Math.87, 2998 (2010)

    MathSciNet  Google Scholar 

  17. A Sevimlican, Math. Probl. Eng.2010, 1 (2010)

    MathSciNet  Google Scholar 

  18. N J Ford, J Xiao and Y Yan, Comp. Methods Appl. Math.12, 273 (2012)

    Google Scholar 

  19. S B Alkahtani, V Gulati and P Goswami, Math. Prob. Eng.2015, 1 (2015)

    Google Scholar 

  20. F A Alawad, E A Yousif and A I Arbab, Int. J. Diff. Eqns.2013, 1 (2013)

    Google Scholar 

  21. M Hanss, Applied fuzzy arithmetic: An introduction with engineering applications (Springer, Berlin, 2005)

    MATH  Google Scholar 

  22. L Jaulin, M Kieffer, O Didrit and E Walter, Applied interval analysis (Springer, France, 2001)

    Google Scholar 

  23. H J Zimmermann, Fuzzy set theory and its application (Kluwer Academic Publishers, London, 2001)

    Google Scholar 

  24. N Mikaeilvand and S Khakrangin, Neural Comp. Appl.21, S307 (2012)

    Google Scholar 

  25. A Khastan, J J Nieto and R Rodrıguez-López, Inform. Sci.222, 544 (2013)

    MathSciNet  Google Scholar 

  26. D Qiu, Wei Zhang and C Lu, Fuzzy Sets Syst.295, 72 (2016)

    Google Scholar 

  27. S Tapaswini, S Chakraverty and T Allahviranloo, Comp. Math. Model.28, 278 (2017)

    Google Scholar 

  28. S Tapaswini, S Chakraverty and J J Nieto, Sadhana42, 45 (2017)

    Google Scholar 

  29. R P Agarwal, V Lakshmikantham and J J Nieto, Nonlinear Anal.: Theory, Methods Appl.72, 2859 (2010)

    Google Scholar 

  30. S Arshad and V Lupulescu, Nonlinear Anal.: Theory, Methods Appl.74, 3685 (2011)

    Google Scholar 

  31. T Allahviranloo, S Salahshour and S Abbasbandy, Soft Comp.16, 297 (2012)

    Google Scholar 

  32. E Khodadadi and E Celik, Fixed Point Theory Appl.2013, 1 (2013)

    Google Scholar 

  33. A Souahi, A G Lakoud and A Hitta, Adv. Fuzzy Syst.2016, 1 (2016)

    Google Scholar 

  34. S Chakraverty and S Tapaswini, Comp. Model. Eng. Sci.103, 71 (2014)

    Google Scholar 

  35. S Chakraverty and S Tapaswini, Chin. Phys. B23, 120202-1 (2014)

    ADS  Google Scholar 

  36. D Behera, S Chakraverty and S Tapaswini, ASCE-ASME J. Risk Uncert. Eng. Systems: Part B. Mech. Eng.1, 041007-1 (2015)

    Google Scholar 

  37. A Rivaz, O S Fard and T A Bidgoli, SeMA J.73, 149 (2016)

    MathSciNet  Google Scholar 

  38. G Adomian, J. Math. Anal. Appl.102, 420 (1984)

    MathSciNet  Google Scholar 

  39. G Adomian, Solving frontier problems of physics: The decomposition method (Kluwer Academic Publishers, Boston, 1994)

    MATH  Google Scholar 

  40. T Allahviranloo and N Taheri, Int. J. Cont. Math. Sci.4, 105 (2009)

    Google Scholar 

  41. S Tapaswini and S Chakraverty, Appl. Soft Comput.24, 249 (2014)

    Google Scholar 

  42. Y Hu, Y Luo and Z Lu, J. Comp. Appl. Math.215, 220 (2008)

    ADS  Google Scholar 

  43. E Babolian, H Sadeghi and S Javadi, Appl. Math. Comput. 149, 547 (2004)

    MathSciNet  Google Scholar 

  44. L Wang and S Guo, World Acad. Sci., Eng. Tech.52, 979 (2011)

    Google Scholar 

  45. K S Miller and B Ross, An introduction to the fractional calculus and fractional differential equations (John Wiley and Sons, New York, 1993)

    MATH  Google Scholar 

  46. K Abbaoui and Y Cherruault, Comput. Math. Appl.28, 103 (1994)

    MathSciNet  Google Scholar 

  47. K Abbaoui and Y Cherruault, Comput. Math. Appl.29, 109 (1995)

    MathSciNet  Google Scholar 

  48. Y Cherruault, Kybernetes18, 31 (1989)

    MathSciNet  Google Scholar 

  49. N Himoun, K Abbaoui and Y Cherruault, Kybernetes28, 423 (1999)

    MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Government Autonomous College, Angul, 759 143, India

    Smita Tapaswini

  2. Department of Mathematics, The University of the West Indies, Mona Campus, Kingston, 7, Jamaica

    Diptiranjan Behera

Authors
  1. Smita Tapaswini
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  2. Diptiranjan Behera
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Correspondence to Diptiranjan Behera.

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Tapaswini, S., Behera, D. Analysis of imprecisely defined fuzzy space-fractional telegraph equations. Pramana - J Phys 94, 32 (2020). https://doi.org/10.1007/s12043-019-1889-x

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  • DOI: https://doi.org/10.1007/s12043-019-1889-x

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