Using reproducing kernel for solving a class of fractional partial differential equation with non-classical conditions

Today, most of the real physical world problems can be best modeled with fractional differential equations. Besides modeling, the solution techniques and their reliabilities are most important. Therefore, high accuracy solutions are always needed. In this paper, a new method is provided to solve fractional partial differential equation in a very favorable reproducing kernel space. It’s reproducing kernel function is discussed in detail. From the examples considered here, it can be easily seen that our method has small computational work, fast convergence speed and high precision.