There are various types of fractional derivatives in literature e.g. Caputo, Riemann–Liouville, conformable and so on. In the present paper, a new integrable nonlinear
Schro¨dinger type equation in (2?1)-dimensions is investigated, which describes the spin
dynamics of Heisenberg ferromagnetic spin chains. Some bright and dark solitons and
other exact solutions of this equation with conformable time fractional derivative are
reported. Then, fractionalize effects of this model are graphically investigated. Moreover,
the simplest equation method and Nucci’s method are utilized for differential equations
with conformable fractional derivatives.