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

Abstract

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.