Abstract
In this paper, we present an alternative representation of the advection–reaction diffusion model involving fractional-order derivatives with Mittag-Leffler kernel. The study includes three main aspects: existence and uniqueness of solutions, Hyers–Ulam stability, and numerical simulations. For the existence and uniqueness of solutions, we use fixed point approach; also, we presents the Hyers–Ulam stability. For the numerical simulations, a new numerical scheme that involve Lagrange interpolation, Laplace transform and forward Euler technique is considered. Numerical simulations were obtained for some specific parameters.
•Existence, uniqueness solutions and Hyers–Ulam stability are obtained.•Atangana–Baleanu fractional derivative with Mittag-Leffler (M-L) kernel is considered.•Numerical simulations are presented for specific parameters.•The ABC-fractional advection–reaction diffusion model has a unique pair of solutions and is HU-stable.