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Research Article

Dynamical behaviours and soliton solutions of the conformable fractional Schrödinger–Hirota equation using two different methods

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Pages 66-74 | Received 30 Jun 2021, Accepted 14 Jan 2022, Published online: 07 Feb 2022

References

  • Baleanu D. About fractional quantization and fractional variational principles. Commun Nonlinear Sci Numer Simul. 2009;14(6):2520–2523.
  • Malomed B. Nonlinear Schrödinger Equations. In: Scott A, editor. Encyclopedia of Nonlinear Science. New York: Routledge; 2005. p. 639–643.
  • Laskin N. Fractional quantum mechanics and Lévy path integrals. Phys Lett A. 2000;268:298–305.
  • Biswas A. Optical solitons: quasi-stationarity versus Lie transform. Opt Quantum Electron. 2003;35:979–998.
  • Eslami M, Rezazadeh H, Rezazadeh M, et al. Exact solutions to the space–time fractional Schrödinger–Hirota equation and the space–time modified KDV–zakharov–Kuznetsov equation. Opt Quantum Electron. 2007;49(279).
  • Kilic B, Inc M. Optical solitons for the Schrödinger–Hirota equation with power law nonlinearity by the bäcklund transformation. Optik (Stuttg). 2017;138:64–67.
  • Rezazadeh H, Mirhosseini-Alizamini SM, Eslami M, et al. New optical solitons of nonlinear conformable fractional Schrödinger-Hirota equation. Optik (Stuttg). 2018;172:545–553.
  • Khalil R, Horani MA, Sababheh AMY. et al. A new definition of fractional derivative. J Comput Appl Math. 2014;264:65–70.
  • Abdeljawad T. On conformable fractional calculus.J Comput Appl Math. 2015;279:57–66.
  • Pinar Z. On the explicit solutions of fractional Bagley–Torvik equation arises in engineering. Int J Optim Control: Theor Appl. 2019;9(3):52–58.
  • Mehreen N, Anwar M. Hermite–Hadamard and Hermite–Hadamard–Fejer type inequalities for p-convex functions via new fractional conformable integral operators. J Math Computer Sci. 2019;19(4):230–240.
  • Korkmaz A, Ersoy Hepson E, Hosseini K, et al. Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class. J King Saud Univ Sci. 2020;32(1):567–574.
  • Khalil R, Al Horani M, Abu Hammad M. Geometric meaning of conformable derivative via fractional cords. J Math Computer Sci. 2019;19(4):241–245.
  • Qi Y, Wang X. Asymptotical stability analysis of conformable fractional systems. J Taibah Univ Sci. 2020;14(1):44–49.
  • Md NA, Tunç C. Constructions of the optical solitons and other solitons to the conformable fractional Zakharov–Kuznetsov equation with power law nonlinearity. J Taibah Univ Sci. 2020;14(1):94–100.
  • Rani M, Ahmed N, Dragomir SS, et al. Some newly explored exact solitary wave solutions to nonlinear inhomogeneous murnaghan’s rod equation of fractional order. J Taibah Univ Sci. 2021;15(1):97–110.
  • Sabi’u J, Jibril A, Gadu AM. New exact solution for the (3 + 1) conformable space–time fractional modified Korteweg–de-Vries equations via sine–cosine method.J Taibah Univ Sci. 2019;13(1):91–95.
  • Younis M, Rizvi STR. Dispersive dark optical soliton in (2 + 1)-dimensions by (G′/G)-expansion with dual-power law nonlinearity. Optik (Stuttg). 2015;126(24):5812–5814.
  • Parkes EJ. Observations on the basic G/G'-expansion method for finding solutions to nonlinear evolution equations. Appl Math Comput. 2010;217:1759–1763.
  • Wazwaz AM. Partial differential equations: methods and applications. Leiden: Balkema; 2002.
  • Wazwaz AM. Partial Differential Equations and Solitary Wave Theory. Beijing and Springer-Verlag Berlin Heidelberg: Higher Education Press; 2009.
  • Akbulut A, Kaplan M. Auxiliary equation method for time-fractional differential equations with conformable derivative. Comput Math with Appl. 2018;75(3):876–882.
  • Vitanov NK. Modified method of simplest equation: powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs. Commun Nonlinear Sci Numer Simul. 2011;16:1176–1185.
  • Yomba E. The extended fan’s sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations. Phys Lett A. 2005;336:463–476.
  • Seadawy AR, Kumar D, Hosseini K, et al. The system of equations for the ion sound and langmuir waves and its new exact solutions. Results Phys. 2018;9:1631–1634.
  • Kumar D, Kaplan M. New analytical solutions of (2 + 1)-dimensional conformable timefractional Zoomeronequation via two distinct technique. Chin J Phys. 2018;56:2173–2185.
  • Liu S, Debbouche A, Wang JR. ILC method for solving approximate controllability of fractional differential equations with noninstantaneous impulses. J Comput Appl Math. 2018;339:343–355.
  • Wang J, Feckan M, Zhou Y. Weakly picard operators method for modified fractional iterative functional differential equations. Fix Point Theory. 2014;15(1):297–310.
  • Hosseini K. Application of the invariant subspace method in conjunction with the fractional sumudu’s transform to a nonlinear conformable timefractional dispersive equation of the fifth-order. Comput Methods Differ Equ. 2019;7(3):359–369.
  • Ullah R, Ellahi R, Sait SM, et al. On the fractional-order model of HIV-1 infection of CD4+ T-cells under the influence of antiviral drug treatment. J Taibah Univ Sci. 2020;14(1):50–59.
  • Ullah R, Ellahi R, Mohyud-Din ST, et al. Exact traveling wave solutions of fractional order boussinesq-like equations by applying Exp-function method. Results Phys. 2018;8:114–120.
  • Liu CS. A new trial equation method and its applications. Commun Theor Phys. 2006;45(3):395–397.
  • Liu CS. Trial equation method to nonlinear evolution equations with rank inhomogeneous: mathematical discussions and its applications. Commun Theor Phys. 2006;45(2):219–223.
  • Odabasi M. Traveling wave solutions of conformable time-fractional Zakharov–Kuznetsov and Zoomeron equations. Chin J Phys. 2020;64:194–202.
  • Odabasi M, Pinar Z, Kocak H. Analytical solutions of some nonlinear fractional-order differential equations by different methods. Math Methods Appl Sci. 2021;44:7526–7537.
  • Pinar Z, Koprulu M O, Kocak H. Symbolic computations for exact solutions of fractional partial differential equations with reaction term. Submitted, 2021.