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The fractional nonlinear convection-diffusion equation and its solution

LIU Yan-qin1,2,XU Ming-yu2 and JIANG Xiao-yun2   

  1. 1. Department of Mathematics, Dezhou Univ., Dezhou 253023, Shandong, China; 2. School of Math. and System Sci., Shandong Univ., Jinan 250100, Shandong, China
  • Received:2006-04-25 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
  • Contact: LIU Yan-qin1,2

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Abstract: Fractional nonlinear convectiondiffusion equation with external forces is given. First, the integer equation is studied by considering the diffusion coefficient D(x)∝xθ. By using the q-exponential function and q-logarithm function, the analytical solution of the equation is derived. Second, a fractional equation with absorption is analyzed. On condition that the nonlinear parameters satisfy certain relationships, a special solution can be obtained. In addition, the asymptotic behaviors for the solution are also discussed.

Key words: Tsallis entropy , q-logarithm function, q-exponential function, fractional calculus, nonlinear equation

CLC Number: 

  • O175.29
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