
AIMS Mathematics, 2019, 4(2): 199214. doi: 10.3934/math.2019.2.199.
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New exact solitary wave solutions to the spacetime fractional differential equations with conformable derivative
1 Department of Mathematics, Jessore University of Science and Technology, Bangladesh
2 Department of Applied Mathematics, University of Rajshahi, Bangladesh
Received: , Accepted: , Published:
Special Issues: New trends of numerical and analytical methods with application to real world models for instance RLC with new nonlocal operators
Keywords: Exact solution; space time fractional modified BBM equation; space time fractional ZKBBM equation; conformable fractional derivative; solitary wave solution
Citation: M. Hafiz Uddin, M. Ali Akbar, Md. Ashrafuzzaman Khan, Md. Abdul Haque. New exact solitary wave solutions to the spacetime fractional differential equations with conformable derivative. AIMS Mathematics, 2019, 4(2): 199214. doi: 10.3934/math.2019.2.199
References:
 1. G. C. Wu, A fractional variational iteration method for solving fractional nonlinear differential equations, Comput. Math. Appl., 61 (2011), 21862190.
 2. J. Ji, J. B. Zhang, Y. J. Dong, The fractional variational iteration method improved with the Adomian series, Appl. Math. Lett., 25 (2012), 22232226.
 3. M. T. Gencoglu, H. M. Baskonus, H. Bulut, Numerical simulations to the noninear model of interpersonal relationship with time fractional derivative, AIP Conf. Proc., 1798 (2017), 020103.
 4. S. Guo, L. Mei, The fractional variational iteration method using He's polynomial, Phys. Lett. A, 375 (2011), 309313.
 5. A. R. Seadawy, Approximation solutions to derivative nonlinear Schrodinger equation with computational applications by variational method, Eur. Phys. J. Plus, 130 (2015), 182.
 6. A. M. A. ElSayed, S. H. Behiry, W. E. Raslan, Adomian's decomposition method for solving an intermediate fractional advectiondispersion equation, Comput. Math. Appl., 59 (2010), 17591765.
 7. A. M. A. ElSayedand, M. Gaber, The Adomian's decomposition method for solving partial differential equation of fractional orderin finite domains, Phys. Lett. A, 359 (2006), 175182.
 8. S.S. Ray, A new approach for the application of Adomian's decomposition method for the solution to fractional space diffusion equation with insulated ends, Appl. Math. Comput., 202 (2008), 544549.
 9. Z. Odibat, S. Momani, A Generalized Differential Transform Method for Linear Partian Differential Equations of fractional Order, Appl. Math. Lett., 21 (2008), 194199.
 10. V. S. Erturk, S. Momani, Z. Odibat, Application of Generalized Transformation Method to Multiorder Fractional Differential Equations, Commun. Nonlinear. Sci., 13 (2008), 16421654.
 11. M. Yavuz, N. Ozdemir, H. M. Baskonus, Solution of fractional partial differential equation using the operator involving nonsingular kernal, Eur. Phys. J. Plus, 133 (2018), 112.
 12. D. Kumar, J. Singh, H. M. Baskonus, et al., An effective computational approach for solving local fractional Telegraph equations, Nonlinear. Sci. Lett. A, 8 (2017), 200206.
 13. M. Dehghan, J. Manafian, The solution of the variable coefficients fourthorder parabolic partial differential equations by homotopy perturbation method, Z. Naturforsch., 64 (2009), 420430.
 14. M. Dehghan, J. Manafian, A. Saadatmandi, Application of semianalytic methods for the FitzhughNagumo equation, which models the transmission of nerve impulses, Math. Meth. Appl. Sci., 33 (2010), 13841398.
 15. A. R. Seadawy, The generalized nonlinear higher order of KdV equations from the higher order nonlinear Schrodinger equation and its solutions, Optic, 139 (2017), 3143.
 16. M. L. Wang, X. Z. Li, J. L. Zhang, The (G'/G)expansion method and the traveling wave solutions to nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372 (2008), 417423.
 17. B. Zhang, (G'/G)expansion method for solving fractional partial differential equation in the theory of mathematical physics, Commun. Theor. Phys., 58 (2012), 623630.
 18. M. A. Akbar, N. H. M. Ali, E. M. E. Zayed, A generalized and improved (G'/G)expansion method for nonlinear evolution equation, Math. Probl. Eng., 20 (2012), 1222.
 19. M. A. Akbar, N. H. M. Ali, E. M. E. Zayed, Abundant exact traveling wave solutions to the generalized Bretherton equation via the improved (G'/G)expansion method, Commun. Theo. Phys., 57 (2012), 173178.
 20. H. M. Baskonusand H. Bulut, Regarding the prototype solutions for the nonlinear fractional order biological population model, AIP Conf. proc., 1738 (2016), 290004.
 21. H. Bulut, G. Yel, H. M. Baskonus, An application of improved Bernoulli subequation function method to the nonlinear time fractional Burgers equation, Tur. J. Math. Comput. Sci., 5 (2016), 117.
 22. M. Foroutan, I. Zamanpour, J. manafian, Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long range interactions, Eur. Phys. J. Plus, 132 (2017), 421.
 23. M. Foroutan, J. Manafian, A. Ranjbaran, Lump solution and its interaction to (3+1)D potentialYTSF equation, Nonlinear. Dynam., 92 (2018), 20772092.
 24. A. Esen, T. A. Sulaiman, H. Bulut, et al. Optical solutions to the space time fractional (1+1)dimensional couple nonlinear Schrodinger equation, Optic, 167 (2018), 150156.
 25. J. Manafian, On the complex structure of the BiswasMilovic equation for power, parabolic and dual parabolic law nonlinearities, Eur. Phys. J. Plus, 130 (2015), 120.
 26. M. Dehghan, J. Manafian, A. Saadatmandi, Analytical treatment of some partial differential equations arising in mathematical physics by using the Expfunction method, Int. J. Mod. Phys. B, 25 (2011), 29652981.
 27. M. A. Akbar, N. H. M. Ali, New solitary and periodic solutions to nonlinear evolution equation by Exp function method, World Appl. Sci. J., 17 (2012),16031610.
 28. B. Lu, Backlund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations, Phys. Lett. A, 376 (2012), 20452048.
 29. S. M. Guo, L. Q. Mei, Y. Li, et al. The improved fractional subequation method and its applications to the spacetime fractional differential equations in fluid mechanics, Phys. Lett. A., 376 (2012), 407411.
 30. S. Zhang, H. Q. Zhang, Fractional subequation method and its application to the nonlinear fractional PDEs, Phys. Lett. A, 375 (2011), 10691073.
 31. B. Lu, The first integral method for some time fractional differential equation, J. Math. Anal. Appl., 395 (2012), 684693.
 32. A. Bekir, O. Guner, O. Unsal, The First Integral Method for exact Solutions to nonlinear Fractional Differential Equation, J. Compt. Nonlinear. Dynam., 10 (2015).
 33. M. H. Uddin, M. A. Akbar, M. A. Khan, et al. Close Form Solutions to the Fractional Generalized Reaction Duffing Model and the Density Dependent Fractional Diffusion Reaction Equation, Appl. Comput. Math., 6 (2017), 177184.
 34. L. X. Li, E. Q. Li, M. L. Wang, The (G'/G)expansion method and its application to travelling wave solutions to the Zakharovequation, Appl. Math. B., 25 (2010), 454462.
 35. E. M. E. Zayed, M. A. M. Abdelaziz, The two variable (G'/G)expansion method for solving the nonlinear KdVmkdV equation, Math. Probl. Eng., 2012 (2012), 725061.
 36. H. M. Baskonus, H. Bulut, On the numerical solutions of some fractional ordinary differential equations by fractional AdamsBashforthMoulton method, Open Math., 13 (2015), 547556.
 37. S. H. Seyedi, B. N. Saray, A. Ramazani, On the multiscale simulation of squeezing nanofluid flow by a highprecision scheme, Power Tech., 340 (2018), 264273.
 38. S. H. Seyedi, B. N. Saray, M. R. H. Nobari, Using interpolation scaling functions based on Galerkin method for solving nonNewtonian fluid flow between two vertical flat plates, Appl. Math. Comput., 269 (2015), 488496.
 39. J. F. Alzaidy, Fractional subequation method and its application to the space time fractional differential equation in mathematical physics, British J. Math. Comput. Sci., 3 (2013), 153163.
 40. S. M. Ege, E. Misirli, The modified Kudryashov method for solving some fractional order nonlinear equations, Adv. Differ. Equations, 2014 (2014).
 41. A. Bekir, O. Guner, O. Unsal, The first integral method for exact solution to nonlinear fractional differential equations, J. Comput. Nonlinear Dynam., 10 (2015) 021020.
 42. M. Song, C. Yang, Exact traveling wave solutions to the ZakharovKuznetsovBenjaminBonaMahony equation, Appl. Math. Comput., 216 (2010), 32343243.
 43. E. Aksoy, M. Kaplan, A. Bekir, Exponential rational function method for space time fractional differential equation, J. Waves Random. Complex Media, 26 (2016) 142151.
 44. M. Ekici, E. M. E. Zayed, A. Sonmezoglu, A new fractional subequation for solving the space time fractional differential equation in mathematical physics, Comput. Methods Differ. Equations, 2 (2014), 153170.
 45. R. Khalil, M. Al Horani, A. Yousef, et al. A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 6570.
 46. Y. Cenesiz, D. Baleanu, A. Kurt, et al. New exact solution to Burgers' type equations with conformable derivative, J. Waves Random. Complex Media, 27 (2016), 103116.
 47. A. M. Wazwaz, Partial Differential Equations and Solitary Wave Theory, New York: Springer, 2009.
 48. S. T. MohyudDin, S. Bibi, Exact solutions for nonlinear fractional differential equations using (G'/G)expansion method, Alexandria Eng. J., 57 (2018), 10031008.
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