An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms

ERSOY HEPSON Ö., KORKMAZ A., HOSSEINI K., REZAZADEH H., ESLAMI M.

Boletim da Sociedade Paranaense de Matemática, cilt.40, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40
  • Basım Tarihi: 2022
  • Doi Numarası: 10.5269/bspm.44592
  • Dergi Adı: Boletim da Sociedade Paranaense de Matemática
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: Sine-Gordon Expansion Method, Conformable time fractional KdV Equation, Conformable time fractional modified KdV Equation, Exact Solution, Traveling Wave Solution, DE-VRIES EQUATION, LUMP SOLUTIONS, WAVE SOLUTIONS
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equations in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions. Some exact solutions in traveling wave forms are explicitly expressed by the proposed method for both the Korteweg-de Vries and modified Korteweg-de Vries equations.