An efficient numerical algorithm for solving nonlinear fractional Volterra integro-differential equation

The goal of this paper is to contribute a firm and outstanding program to nonlinear fractional Volterra integro-differential equations with the initial value problem on the basis of the reproducing kernel method (RKM). To a certain extent, the difficulty of preserving memory of fractional differential operators is reduced. At the beginning, the model can be converted to the equivalent fractional Volterra integro-differential problem with a singular kernel that is consistent with the characteristics of Caputo derivatives. Additionally, the quasi-Newton’s method (QNM) and the principles of the least-squares method (LSM) are used to linearize the model and obtain the operation matrix, respectively. Once again, the uniqueness of the \(\varepsilon \) $\epsilon$ approximate solution is proven at length. The convergence and error estimation of the new technique are also deliberated. In the final step, the effectiveness of the algorithm is demonstrated by numerical examples.