Designing an efficient algorithm for fractional partial integro-differential viscoelastic equations with weakly singular kernel

In this paper, the discretization method is developed by means of Mott-fractional Mott functions (MFM-Fs) for solving fractional partial integro-differential viscoelastic equations with weakly singular kernels. By taking into account the Riemann-Liouville fractional integral operator and operational matrix of integration, we convert the proposed problem to fractional partial integral equations with weakly singular kernels. It is necessary to mention that the operational matrices of integration are obtained with new numerical algorithms. These changes effectively affect the solution process and increase the accuracy of the proposed method. Besides, we investigate the error analysis of the approach. Finally, several examples are solved by applying the discretization method by combining MFM-Fs and the gained results are compared with the methods available in the literature.