## An algorithm for solving the fractional convection-diffusion equation with nonlinear source term.(English)Zbl 1118.35301

Summary: An algorithm based on Adomian’s decomposition method is developed to approximate the solution of the nonlinear fractional convection-diffusion equation $\frac{\partial^\alpha u}{\partial t^\alpha}=\frac{\partial^2u} {\partial x^2}-c\frac{\partial u}{\partial x}+\Psi(u)+f(x,t),\quad 0<x<1,\;0< \alpha\leq 1,\;t>0.$ The fractional derivative is considered in the Caputo sense. The approximate solutions are calculated in the form of a convergent series with easily computable components. The analysis is accompanied by numerical examples and the obtained results are found to be in good agreement with the exact solutions, known for some special cases.

### MSC:

 35A25 Other special methods applied to PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35A35 Theoretical approximation in context of PDEs 26A33 Fractional derivatives and integrals