Stability analysis for fractional order advection–reaction diffusion system

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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.