Computational method for solving nonlinear voltera integro-differential equations

In this article, we give numerical solution using reproducing kernel Hilbert space method for integrodifferential equations which represent the charged particle motion for certain configurations of oscillating magnetic fields in the sense of the Caputo fractional derivative of order 1<α ≤2. The solution is determined by a convergent series with easily computable components. Three examples are given to demonstrate the efficiency of this method. Graphical results, tabulate data, and numerical comparisons are presented and discussed quantitatively to illustrate the solutions.