Analysis and numerical simulation of multicomponent system with Atangana-Baleanu fractional derivative

In this paper, we consider the mathematical analysis and numerical simulation of time-fractional multicomponent systems. Here, the classical time derivatives in such systems are replace with the Atangana-Baleanu fractional derivative in the sense of Caputo. This derivative is found useful in the sense that it combines both the non-local and nonsingular kernels in its formulation. A two-step family of Adams-Bashforth method is derived for the approximation of the Atangana-Baleanu derivative. Numerical experiments presented for different instances of α, 0 < α ≤ 1 correspond to our theoretical findings.