Lie symmetries, symmetry reductions and conservation laws of time fractional modified Korteweg-de Vries (mkdv) equation

Akbulut A., Tasan F.

CHAOS SOLITONS & FRACTALS, vol.100, pp.1-6, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 100
  • Publication Date: 2017
  • Doi Number: 10.1016/j.chaos.2017.04.020
  • Journal Name: CHAOS SOLITONS & FRACTALS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-6
  • Keywords: Fractional differential equations, Fractional lie group method, Lie symmetries, DIFFERENTIAL-EQUATIONS, BURGERS
  • Bursa Uludag University Affiliated: No

Abstract

In this work, we study Lie symmetry analysis for fractional order differential equations that is one of the applications of symmetries. This study deals with Lie symmetry of fractional order modified Korteweg-de Vries (mKdV) equation. We found Lie symmetries of this equation and then we reduced fractional order modified Korteweg-de Vries (mKdV) equation to fractional order ordinary differential equation with Erdelyi-Kober fractional differential operator. Then we used characteristic method for fractional order differential equations and help of founded these Lie symmetries for finding solutions for given equation. Then we obtained infinite and finite conservation laws of fractional order modified Korteweg-de Vries (mKdV) equation. (C) 2017 Elsevier Ltd. All rights reserved.