Fractional modified Kawahara equation with Mittag–Leffler law

In this work, we study a fractional extension of modified Kawahara equation by using Atangana–Baleanu fractional operator in the sense of Caputo (ABC). The fractional modified Kawahara equation is very useful to describe plasma waves and capillary-gravity water waves. We show existence and uniqueness of the solution of fractional modified Kawahara equation by making use of the fixed-point theorem. We obtain the solution of the fractional modified Kawahara equation with aid of the homotopy analysis transform technique. The outcomes of the investigation are demonstrated in graphical and tabular forms to show the influence of order of ABC fractional operator and variables on the displacement profile.