An efficient technique based on least-squares method for fractional integro-differential equations

In this paper, we investigate an efficient technique for solving fractional integro-differential equations (FIDEs) that have numerous applications in various fields of science. The proposed technique is based upon the Legendre orthonormal polynomial and least Csquares method (LSM). By dividing the domain into n cells, a k-th order polynomial approximate solution in each cell can be obtained by LSM. The unique solvability and stability of the proposed numerical scheme are proven by analyzing the condition number of the matrix of the linear system. Moreover, the optimal convergence order under W22-norm is provided as well. Numerical examples are studied to verify our theoretical discovery. Comparison with the traditional reproducing kernel method and C3-spline method illustrates that our algorithm can obtain a more accurate approximating solution.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

In this paper, an efficient technique for solving fractional integro-differential equations (FIDEs) is investigated, which has numerous applications in various fields of science. The proposed technique is based on the Legendre orthonormal polynomial and least squares method (LSM). By dividing the domain into cells, a polynomial approximate solution can be obtained in each cell by LSM. The solvability and stability of the proposed numerical scheme are proven, and the optimal convergence order under W22-norm is provided. Numerical examples verify the theoretical discovery and show the superiority of the proposed algorithm compared to traditional methods.