Numerical Solution of a Wave Partial Differential Equation With the Caputo-Fabrizio Time-Fractional Derivative Using the Finite Element Method Under Non-Homogenous Dirichlet and Neumann Boundary Conditions - Boutiba, Malika; Baghli-Bendimerad, Selma; Sabit, Souhila (Armenian Journal of Mathematics, 2026)
In the present article, we propose a numerical resolution of the Caputo-Fabrizio temporal fractional wave equation with non-homogenous Dirichlet and Neumann functional conditions. We derive and analyze the semi- and fully discrete approximations using the introduced finite difference scheme for the time Caputo-Fabrizio derivative and the finite element scheme for the spacial derivative. Result of the existence and uniqueness of the solution is discussed, stability and error estimates are established. To support the theoretical studies, a numerical example is given.
Keywords: Finite Element Method; Caputo--Fabrizio Derivative; Time Fractional Wave Equation; Error Estimates; Stability; Convergence Analysis