New Analytical Solutions of Conformable Time Fractional Bad and Good Modified Boussinesq Equations

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Durur H., TAŞBOZAN O., Kurt A.

Applied Mathematics and Nonlinear Sciences, cilt.5, sa.1, ss.447-454, 2020 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2478/amns.2020.1.00042
  • Dergi Adı: Applied Mathematics and Nonlinear Sciences
  • Derginin Tarandığı İndeksler: Scopus, Applied Science & Technology Source, Compendex, zbMATH, DIALNET
  • Sayfa Sayıları: ss.447-454
  • Anahtar Kelimeler: auxiliary equation method, bad and good modified Boussinesq equations, conformable fractional derivative
  • Hatay Mustafa Kemal Üniversitesi Adresli: Evet

Özet

The main purpose of this article is to obtain the new solutions of fractional bad and good modified Boussinesq equations with the aid of auxiliary equation method, which can be considered as a model of shallow water waves. By using the conformable wave transform and chain rule, nonlinear fractional partial differential equations are converted into nonlinear ordinary differential equations. This is an important impact because both Caputo definition and Riemann-Liouville definition do not satisfy the chain rule. By using conformable fractional derivatives, reliable solutions can be achieved for conformable fractional partial differential equations.