Discretisation of fractional calculus operator based on polynomial solution

In order to solve the problem of poor performance of traditional calculus operator discretisation methods in discretising multivariate continuous attributes, this study uses polynomial solution to investigate a new discretisation method for fractional calculus operators. Combining approximate algorithms to set up approximate methods for fractional calculus operators, the discretisation of fractional calculus operators is achieved by discretising the continuous properties of single and multiple variables. The results show that when (x, k) takes values of (9/10, 9/10), the method proposed in this study obtained an exact solution of 0.853815, while the exact solutions of other methods were only 0.488736 and 0.357617. This method can obtain exact solutions of calculus operators of several orders, and the discretisation process has stronger approximation performance, which has important practical significance for numerical calculations and theoretical research in related fields.