Solvability of the fractional Volterra-Fredholm integro differential equation by hybridizable discontinuous Galerkin method

Abstract

This article proves the existence and uniqueness of the solution obtained by the hybridizable discontinuous Galerkin (HDG) method of the fractional Volterra-Fredholm integro differential equation. The method based on local solvers and transmission condition is applied to the equation using two auxiliary variables. The form of the equation is amenable for achieving the solvability criteria of the problem according to the HDG method. We also calculate a numerical solution of the problem whose exact solution is taken as a smooth or fractional function. This results in a tridiagonal, symmetric, and positive definite stiffness matrix.