Akgul, AliModanli, Mahmut2024-12-242024-12-2420221555-14231555-1415https://doi.org/10.1115/1.4053036https://hdl.handle.net/20.500.12604/7173In this paper, we research the fractional telegraph equation with the Atangana-Baleanu-Caputo derivative. We use the Laplace method to find the exact solution of the problems. We construct the difference schemes for the implicit finite method. We prove the stability of difference schemes for the problems by the matrix method. We demonstrate the accuracy of the method by some numerical experiments.eninfo:eu-repo/semantics/closedAccessAtangana-Baleanu derivativeLaplace methodstability inequalitiesdifference schemesimplicit finite methodArticle172Q3WOS:000733403800001Q12-s2.0-8512742381710.1115/1.4053036