Numerical approximation for generalized fractional Volterra integro-differential equations via parabolic contour

In this article, a numerical scheme is constructed to approximate the generalized fractional Volterra integro-differential equations with the regularized Prabhakar derivative. The solution of the problem is represented in the form of inverse Laplace transform in the complex plane.Then we select the parabolic contour as an optimal contour and use trapezoidal rule to approximate the inverse Laplace transform.Next, the performance of the numerical scheme is implemented for an example. Further, we obtain the absolute errors for various parameters by using our numerical scheme on parabolic contour and show that the proposed algorithm for the solution of inverse Laplace transform is a very well algorithm with high order accuracy.

کلیدواژه ها:

Laplace Transforms ، Parabolic contour ، Generalized fractional Volterra integro-differential equations