Wavelet method for time-fractional convection-diusion equations

In this paper, a new method based on the Bernoulli wavelets expansion together with operational matrix of fractional integration is proposed to solve time-fractional partial di erential equations. The proposed method is very convenient for solving such problems, since the initial and boundary conditions are taken into account automatically. The suggested method reduces this type of equation to the solution of a algebraic system. They have been used in modeling turbulent flow chaotic dynamics of classical conservation systems.

Keywords:

Bernoulli wavelet , time-fractional partial di erential equations , Collocation method , Caputo derivative .