Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equations

A numerical method based on fractional B-spline is developed and examined to approximate the solution of fractional multiterm pantograph equations. The method is applied to a uniform partition, and the midpoints of the partition are used as extra points to construct a uniquely solvable system. Convergence analysis of the method is discussed via Green’s function approach, and an error bound dependent on the regularity of the exact solution is obtained. Additionally, to demonstrate the efficiency and accuracy of the proposed method, several examples are solved. The results indicate that the practical orders of convergence obtained by our proposed method are in good agreement with the theoretical results.