Based on the smoothed particle hydrodynamics (SPH) method, the SPH method without kernel function derivative (KDF-SPH) is applied to the numerical solution of the time fractional convection-diffusion equation. In the simulation process of the time fractional convection-diffusion equation, the finite difference method (FDM) is used for the Caputo time fractional derivative, and the KDF-SPH method and SPH method are used for the spatial derivative respectively. The results show that the error of KDF-SPH method is much smaller than that of SPH method. Compared with the SPH method, KDF-SPH retains all the advantages of SPH (meshless, Lagrangian and particle properties). This method plays a great role in reducing errors and maintaining stability, and numerical approximation can be carried out regardless of whether the kernel gradient exists or not. It avoids the calculation of the derivative of the kernel function, reduces the requirement for the derivability of the kernel function, improves the calculation efficiency and is easy to be programmed. It is easy to expand the calculation of high-dimensional problems and has good practical application value.

Considering influence factors of virtual particle method in solving boundary problems, such as the increase of redundant calculation due to the large amount of particle search, we adopt SPH correction method in calculation domain, and use finite difference method at boundary, to realize a SPH boundary processing algorithm based on finite difference method. Taking the heat conduction problem as an example, the numerical simulation results are verified. It shows that as the proposed boundary treatment method is used to solve fixed and convective boundary heat conduction problems, numerical solution is in good agreement with analytical solution, and the numerical simulation process is reliable and effective. Advantages of the two algorithms complement each other, which provides a new idea for treatment of related boundary value problems.