A new method for solving hypersingular integral equations of the first kind

A simple and efficient method for solving hypersingular integral equations of the first kind in reproducing kernel spaces is developed. In order to eliminate the singularity of the equation, a transform is used. By improving the traditional reproducing kernel method, which requires the image space of the operator to be W21 and the operator to be bounded, the exact solutions and the approximate solutions of hypersingular integral equations of the first kind are obtained. The advantage of this numerical method lies in the fact that, on one hand, the approximate solution is continuous, and on the other hand, the approximate solution converges uniformly and rapidly to the exact solution. The validity of the method is illustrated with two examples.