TRAVELLING WAVE SOLUTIONS FOR THE TIME-FRACTIONAL EQUATIONS BY THE SINE-GORDON EXPANSION METHOD

ÜNAL M.

Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, cilt.15, sa.1, ss.215-228, 2025 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 1
  • Basım Tarihi: 2025
  • Dergi Adı: Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.215-228
  • Anahtar Kelimeler: Caudrey-Dodd-Gibbon-Kotera-Sawada equation, Hirota Satsuma equation, Sine-Gordon expansion method, travelling wave solution
  • Uşak Üniversitesi Adresli: Evet

Özet

The aim of this paper is to explore travelling wave solutions by utilising the novel sine-Gordon expansion method for the time-fractional (1 + 1)-dimensional Hirota Satsuma equation and the time-fractional (2 + 1) -dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equations. Using the traveling wave transformation, the fractional PDE turns into an ODE. Applying the auxiliary equation from the described method, we get an algebraic polynomial, setting the like power to zero, we get a system of algebraic equations. Solving these equations by using mathematical software program, we acquire the solution sets for the constants. Abundant travelling wave solutions are obtained and expressed in terms of hyperbolic functions. Some graphics of the solutions have also been presented. The proposed method is direct and effective in solving nonlinear evolution equations.