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Chin. Phys. B, 2014, Vol. 23(7): 070505    DOI: 10.1088/1674-1056/23/7/070505
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Space–time fractional KdV–Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

Emad K. El-Shewy, Abeer A. Mahmoud, Ashraf M. Tawfik, Essam M. Abulwafa, Ahmed Elgarayhi
Theoretical Physics Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
Abstract  The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non-thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.
Keywords:  dust-acoustic waves      reductive perturbation method      modified Riemann-Liouville fractional derivative      space-time fractional KdV-Burgers equation     
Received:  11 September 2013      Published:  15 July 2014
PACS:  05.45.Df (Fractals)  
  52.30.-q (Plasma dynamics and flow)  
  52.27.Lw (Dusty or complex plasmas; plasma crystals)  
  52.35.Fp (Electrostatic waves and oscillations (e.g., ion-acoustic waves))  
Corresponding Authors:  Essam M. Abulwafa     E-mail:  abulwafa@mans.edu.eg
About author:  05.45.Df; 52.30.-q; 52.27.Lw; 52.35.Fp

Cite this article: 

Emad K. El-Shewy, Abeer A. Mahmoud, Ashraf M. Tawfik, Essam M. Abulwafa, Ahmed Elgarayhi Space–time fractional KdV–Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions 2014 Chin. Phys. B 23 070505

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