On the phase separation in the ternary alloys: Numerical and computational simulations of the Atangana–Baleanu time‐fractional Cahn–Allen equation

Abstract

AbstractThis article gives a survey on computational and numerical solutions for the phase separation in Fe‐Cr‐X (X = Mo, Cu) ternary alloys. This separation is mathematically given by the Atangana–Baleanu time‐fractional Cahn–Allen equation. The generalized Kudryashov, sech–tanh, and the Adomian decomposition approaches are employed to get a bundle of analytical and numerical solutions. The obtained analytical solutions are used to evaluate the initial and boundary conditions of the phase ternary alloys separation operation. Moreover, the stability property of solutions is investigated based on the characteristics of the Hamiltonian system. Novel properties of the investigated model are figured out by distinct types of sketches. Finally, the accuracy of both used computational schemes is illustrated.