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Exact traveling wave solutions of density-dependent conformable space–time-fractional diffusion–reaction equation with quadratic nonlinearity

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Abstract

By using improved F-expansion method (IFEM), we study density-dependent space–time-fractional diffusion–reaction equation with quadratic nonlinearity (DDFDRE), which arises in mathematical biology. The fractional derivative is described in the sense of the CF derivative. Exact traveling wave solutions for DDFDRE are derived and expressed in terms of hyperbolic functions and rational functions. The IFEM is brief, efficient and easy to apply. It also can be used to solve many other fractional nonlinear evolution equations.

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References

  1. I Podlubny Fractional Differential Equations (San Diego: Academic Press) (1999)

    MATH  Google Scholar 

  2. B Ross Fractional Calculus and Its Applications (New York: Springer) (1975)

    Google Scholar 

  3. S Das Functional Fractional Calculus (New York: Springer) (2011)

    MATH  Google Scholar 

  4. M Safari, D D Ganji and M Moslemi Comput. Math. Appl. 58 2091 (2009)

    MathSciNet  Google Scholar 

  5. J S Duan, R Rach, D Baleanu and A M Wazwaz Commun. Fract. Calc. 3 73 (2012)

    Google Scholar 

  6. J Biazar and M Eslami Int. J. Phys. Sci. 6 1203 (2011)

    Google Scholar 

  7. K R Raslan, A Biswas and Z F A Sheer Int. J. Phys. Sci. 7 1412 (2012)

    Google Scholar 

  8. Z Z Ganji, D D Ganji, H Jafari and M Rostamian Topol. Methods Nonlinear Anal. 31 341 (2008)

    MathSciNet  Google Scholar 

  9. Z Z Ganji, D D Ganji, H Jafari and M Rostamian Numer. Methods Partial Differ. Equ. 26 117 (2010)

    Google Scholar 

  10. H Aminikhah, A H R Sheikhani and H Rezazadeh Ain Shams Eng. J. 9 581 (2018)

    Google Scholar 

  11. H Yépez-Martínez, J M Reyes and I O Sosa Br. J. Math. Comput. Sci. 4 572 (2014)

    Google Scholar 

  12. M Mirzazadeh, M Eslami and A Biswas Pramana 82 465 (2014)

    ADS  Google Scholar 

  13. H Yépez-Martínez, I O Sosa and J M Reyes J. Appl. Math. 2015 191545 (2015)

  14. H Aminikhah, A H R Sheikhani and H Rezazadeh Nonlinear Eng. 4 15 (2015)

    ADS  Google Scholar 

  15. M Mirzazadeh, M Ekici and A Sonmezoglu Iran. J. Sci. Technol. Trans. A Sci. 41 819 (2017)

    MathSciNet  Google Scholar 

  16. N Taghizadeh, M Mirzazadeh, M Rahimian and M Akbari Ain Shams Eng. J. 4 897 (2013)

    Google Scholar 

  17. S S Ganji, D D Ganji, and S Karimpour Prog. Electromagn. Res. C 5 21 (2008)

    Google Scholar 

  18. G Jumarie Comput. Math. Appl. 51 1367 (2006)

    MathSciNet  Google Scholar 

  19. J H He Int. J. Theor. Phys. 53 3698 (2014)

    Google Scholar 

  20. R Hilfer Applications of Fractional Calculus in Physics (Singapore: World Scientific) (2000)

    MATH  Google Scholar 

  21. R Khalil, M Al Horani, A Yousef and M Sababheh J. Comput. Appl. Math. 264 65 (2014)

    MathSciNet  Google Scholar 

  22. T Abdeljawad J. Comput. Appl. Math. 279 57 (2015)

    MathSciNet  Google Scholar 

  23. W S Chung J. Comput. Appl. Math. 290 150 (2015)

    MathSciNet  Google Scholar 

  24. H Rezazadeh, H Aminikhah and A H R Sheikhani Iran. J. Numer. Anal. Optim. 7 13 (2017)

    Google Scholar 

  25. H Aminikhah, A H R Sheikhani and H Rezazadeh Sci. Iran. B 23 1048 (2016)

    Google Scholar 

  26. H Rezazadeh and B P Ziabarya Comput. Res. Prog. Appl. Sci. Eng. 2 106 (2016)

    Google Scholar 

  27. M Eslami and H Rezazadeh Calcolo 53 475 (2016)

    MathSciNet  Google Scholar 

  28. K Hosseini, P Mayeli and R Ansari Opt. Int. J. Light Electron Opt. 130 737 (2017)

    Google Scholar 

  29. K Hosseini, P Mayeli and R Ansari Waves Random Complex Media 28 426 (2018)

    MathSciNet  ADS  Google Scholar 

  30. H Tariq and G Akram Nonlinear Dyn. 88 581 (2017)

    Google Scholar 

  31. A Neamaty, B Agheli and R Darzi SeMA J. 73 121 (2016)

    MathSciNet  Google Scholar 

  32. N Taghizadeh and M N Foumani Appl. Appl. Math. 11 943 (2016)

    MathSciNet  Google Scholar 

  33. A Korkmaz and K Hosseini Opt. Quantum Electron. 49 278 (2017)

    Google Scholar 

  34. A Korkmaz J. Comput. Nonlinear Dyn. 13 081004 (2018)

    Google Scholar 

  35. A Korkmaz Chaos Solitons Fractals 96 132 (2017)

    MathSciNet  ADS  Google Scholar 

  36. H Rezazadeh, J Manafian, F S Khodadad, and F Nazari Opt. Quantum Electron. 50 121 (2018)

    Google Scholar 

  37. H Rezazadeh, A Korkmaz, M Eslami, J Vahidi and R Asghari Opt. Quantum Electron. 50 150 (2018)

    Google Scholar 

  38. A Korkmaz Waves Random Complex Media 29 124 (2019)

    MathSciNet  ADS  Google Scholar 

  39. H Rezazadeh, M S Osman, M Eslami, M Ekici, A Sonmezoglu et al. Optik 164 84 (2018)

    ADS  Google Scholar 

  40. A Korkmaz Commun. Theor. Phys. 67 479 (2017)

    ADS  Google Scholar 

  41. M S Osman Nonlinear Dyn. 96 1491 (2019)

    Google Scholar 

  42. M S Osman, D Lu and M M A Khater Results Phys. 13 102157 (2019)

    Google Scholar 

  43. A Javid, N Raza, and M S Osman Commun Commun. Theor. Phys. 71 362 (2019)

    ADS  Google Scholar 

  44. M S Osman, B Ghanbari and J A T Machado Eur. Phys. J. Plus 134 20 (2019)

    Google Scholar 

  45. B Ghanbari, M S Osman and D Baleanu Mod. Phys. Lett. A 34 1950155 (2019)

    ADS  Google Scholar 

  46. H I Abdel-Gawad, N S. Elazab and M S Osman J. Phys. Soc. Jpn. 82 044004 (2013)

    ADS  Google Scholar 

  47. H I Abdel-Gawad and M S Osman J. Adv. Res. 6 593 (2015)

    Google Scholar 

  48. M S Osman and B Ghanbari Opt. Int. J. Light Electron Opt. 175 328 (2018)

    Google Scholar 

  49. M S Osman and J A T.Machado J. Electromagn. Waves Appl. 32 1457 (2018)

    Google Scholar 

  50. H I Abdel-Gawad and M S Osman Kyungpook Math. J. 53 661 (2013)

    MathSciNet  Google Scholar 

  51. M S Osman Pramana J. Phys. 88 67 (2017)

    ADS  Google Scholar 

  52. M S Osman, H I Abdel-Gawad and M A El Mahdy Results Phys. 8 1054 (2018)

    ADS  Google Scholar 

  53. M S Osman and J A T.Machado Nonlinear Dyn. 93 733 (2018)

    Google Scholar 

  54. H Rezazadeh, M S Osman, M Eslami, M Mirzazadeh, Q Zhou, S A Badri and A Korkmaz Nonlinear Eng. 8 224 (2018)

    ADS  Google Scholar 

  55. K U Tariq, M Younis, H Rezazadeh, S T R Rizvi and M S Osman Mod. Phys. Lett. B 32 1850317 (2018)

    ADS  Google Scholar 

  56. W Sikander, U Khan, N Ahmed and S T Mohyud-Din Results Phys. 7 216 (2017)

    ADS  Google Scholar 

  57. U Khan, R Ellahi, R Khan and S T Mohyud-Din Opt. Quantum Electron. 49 362 (2017)

    Google Scholar 

  58. S T Mohyud-Din Rev. Unión Mat. Argent. 52 143 (2011)

    Google Scholar 

  59. A Ali, M A Iqbal and S T Mohyud-Din Pramana J. Phys. 87 79 (2016)

    ADS  Google Scholar 

  60. J Ahmad and S T Mohyud-Din Math. Phys. PLoS ONE 12 9 (2014)

    Google Scholar 

  61. M Shakeel, Q M Ul-Hassan, J Ahmad, and T Naqvi Adv. Math. Phys. 2014 Article ID 181594 (2014)

  62. A. Yildirim, S T Mohyud-Din, D H Zhang Comput. Math. Appl. 59 2473 (2010)

    MathSciNet  Google Scholar 

  63. S T Mohyud-Din, A Yıldırım and S A Sezer Int. J. Numer. Methods Heat Fluid Flow 21 822 (2011)

    Google Scholar 

  64. M B A Mansour Rep. Math. Phys. 66 375 (2010)

    MathSciNet  ADS  Google Scholar 

  65. M Eslami, B F Vajargah, M Mirzazadeh and A Biswas Indian J.Phys. 88 177 (2014)

    ADS  Google Scholar 

  66. O Güner and A Bekir Int. J. Biomath. 8 1550003 (2015)

    MathSciNet  Google Scholar 

  67. M S Islam, K Khan, M A Akbar and A Mastroberardino R. Soc. Open Sci. 1 140038 (2014)

    ADS  Google Scholar 

  68. M S Islam, K Khan and M A Akbar J. Egypt. Math. Soc. 25 13 (2017)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Modern Technologies Engineering, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

  2. Department of Mathematics, Çankırı Karatekin University, Çankırı, Turkey

    Alper Korkmaz

  3. Universidad Autónoma de la Ciudad de México, Prolongación San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, C.P. 09790, Mexico, D.F., Mexico

    Huitzilin Yépez-Martínez

  4. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    Mostafa Eslami

  5. Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030, Eskisehir, Turkey

    Ahmet Bekir

Authors
  1. Hadi Rezazadeh
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  2. Alper Korkmaz
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  3. Huitzilin Yépez-Martínez
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  4. Mostafa Eslami
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  5. Ahmet Bekir
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Correspondence to Ahmet Bekir.

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Rezazadeh, H., Korkmaz, A., Yépez-Martínez, H. et al. Exact traveling wave solutions of density-dependent conformable space–time-fractional diffusion–reaction equation with quadratic nonlinearity. Indian J Phys 94, 1573–1580 (2020). https://doi.org/10.1007/s12648-019-01597-2

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  • DOI: https://doi.org/10.1007/s12648-019-01597-2

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