On new analytical solutions of fractional systems in shallow water dynamics

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Bakicierler G., Misirli E.

REVISTA MEXICANA DE FISICA, cilt.68, sa.5, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 68 Sayı: 5
  • Basım Tarihi: 2022
  • Doi Numarası: 10.31349/revmexfis.68.050701
  • Dergi Adı: REVISTA MEXICANA DE FISICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, DIALNET
  • Anahtar Kelimeler: Nonlinear fractional partial differential equation, shallow water wave, analytical wave solution, conformable fractional derivative, RATIONAL-FUNCTION METHOD, TRAVELING-WAVE SOLUTION, WHITHAM-BROER-KAUP, BOUSSINESQ, EQUATIONS
  • Marmara Üniversitesi Adresli: Hayır

Özet

Recently, fractional calculus has considerable attention from researchers since many problems in natural sciences and engineering are modelled with differential equations having fractional order. The nonlinear coupled time-fractional Boussinesq-Burger (B-B) equation, the nonlinear time-fractional approximate long water wave (ALW) equation, and the nonlinear (2 + 1)-dimensional space-time fractional generalized Nizhnik-Novikov-Veselov (GNNV) equation are used to express the structure of shallow water waves (SWWs) with different distributions. The analytical solutions of these equations play a substantial role in explaining the properties of complex phenomena in applied sciences. In the current work, we utilize the exponential rational function (ERF) method with the definition of fractional derivative in the conformable sense to achieve new exact traveling wave solutions of these fractional systems. The correctness, validity, and graphics of the new traveling wave solutions are achieved with the aid of Mathematica. Results demonstrate the effectiveness and strength of this technique to solve the system of fractional differential equations (FDEs).