The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Manafian J., İlhan O. A. , Avazpour L.

International Journal Of Nonlinear Sciences And Numerical Simulation, cilt.22, sa.1, ss.1-19, 2021 (SCI Expanded İndekslerine Giren Dergi)

  • Cilt numarası: 22 Konu: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1515/ijnsns-2019-0279
  • Dergi Adı: International Journal Of Nonlinear Sciences And Numerical Simulation
  • Sayfa Sayıları: ss.1-19

Özet

In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered. These models are including (space-time fractional order Boussinesq equation; the space-time (2+1)-dimensional breaking soliton equations; spacetime fractional order SRLW equation) which describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense of β-derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations (ODEs) by the help of transformation β-derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions: solitary, topological, dark soliton, periodic, kink, and rational fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forh.