On the Solution of Burgers' Equation with the New Fractional Derivative

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Kurt A., Çenesiz Y., TAŞBOZAN O.

Open Physics, vol.13, no.1, pp.355-360, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.1515/phys-2015-0045
  • Journal Name: Open Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.355-360
  • Keywords: Conformable Fractional Derivative, Homotopy Analysis Method, Hopf-Cole Transform, Time Fractional Burgers' Equation, Time Fractional Heat Equation
  • Hatay Mustafa Kemal University Affiliated: Yes

Abstract

Firstly in this article, the exact solution of a time fractional Burgers' equation, where the derivative is conformable fractional derivative, with dirichlet and initial conditions is found byHopf-Cole transform. Thereafter the approximate analytical solution of the time conformable fractional Burger's equation is determined by using a Homotopy Analysis Method(HAM). This solution involves an auxiliary parameter which we also determine. The numerical solution of Burgers' equation with the analytical solution obtained by using the Hopf-Cole transform is compared.