The Solutions Of Two Kinds Of Time Fractional Partial Differential Equations

The study of fractional partial differential equations occupies a very im-portant position in various areas of mathematics,and many different methods are introduced to construct exact solutions of fractional partial differential e-quations.In this paper?the exact solutions and analytical solutions of the time fractional partial differential equations are constructed under the Lie symmetry analysis and invariant subspace method.The expressions of the solutions of the space-time fractional partial differential equations are studied.The results are as follows:1.The time-fractional Keller-Segel equations is transformed into the gen-eralized time-fractional Burgers equation with some transform.The separation variables method,homogeneous balance method and invariant subspace method are used to study the solution of the Burgers equation.The expressions for the solutions of the time fractional Keller-Segel equations are established2.Applying the Lie symmetry analysis to the parabolic-elliptic time frac-tional Keller-Segel equations and the time fractional single-walled carbon nan-otube equations?we obtain the group invariant solutions and the conservation laws of the above equations.Applying the invariant subspace method we obtain the analytic solutions of these two equations3.The partial differential equations with both fractional order in time and space are further investigated?and the simplified space-time fractional-order or-dinary differential equations are solved.The expressions of the explicit solutions of some space-time fractional differential equations are obtained.