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

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...

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Published inApplied mathematics and nonlinear sciences Vol. 5; no. 1; pp. 447 - 454
Main Authors Durur, Hülya, Tasbozan, Orkun, Kurt, Ali
Format Journal Article
LanguageEnglish
Published Beirut Sciendo 01.01.2020
De Gruyter Poland
Subjects
26A33
auxiliary equation method
bad and good modified Boussinesq equations
conformable fractional derivative
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Abstract 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.
AbstractList 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.
Author Durur, Hülya
Kurt, Ali
Tasbozan, Orkun
Author_xml – sequence: 1
  givenname: Hülya
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  fullname: Durur, Hülya
  email: hulyadurur@ardahan.edu.tr
  organization: Department of Computer Engineering, Faculty of Engineering, Ardahan University, Ardahan, Turkey
– sequence: 2
  givenname: Orkun
  surname: Tasbozan
  fullname: Tasbozan, Orkun
  organization: Department of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Hatay, Turkey
– sequence: 3
  givenname: Ali
  surname: Kurt
  fullname: Kurt, Ali
  organization: Department of Mathematics, Faculty of Science and Art, Pamukkale University, Denizli, Turkey
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SubjectTerms 26A33
auxiliary equation method
bad and good modified Boussinesq equations
conformable fractional derivative
Title New Analytical Solutions of Conformable Time Fractional Bad and Good Modified Boussinesq Equations
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