Multiquadric quasi-interpolation method for fractional integral-differential equations

In this paper, Multiquadric quasi-interpolation method is used to approximate fractional integral equations and fractional differential equations. Firstly, we construct two operators for approximating the Hadamard integral-differential equation based on quasi interpolators, and verify their properties and order of convergence. Secondly, we obtain that the approximation order of the integral scheme is 3, and the approximation order of the differential scheme is $3-\mu$ for $\mu(0<\mu<1)$ order fractional Hadamard derivative. Finally, The results of numerical experiments show that the numerical results are in greement with the theoretical analysis.