Abstract
The aim of this study is to consider solving an important mathematical model of fractional order ([Formula: see text])-dimensional breaking soliton (Calogero) equation by Khater method. The derivatives are in the local fractional derivative sense. The fractional transformation equation is utilized to convert the proposed nonlinear fractional order differential equation into nonlinear ordinary differential equation. The Khater method is used to construct the closed-form traveling wave solutions of the said fractional differential equation. In addition, many new exact solutions are constructed. This shows that the Khater method is more convenient, powerful, and easy to solve the nonlinear fractional differential equation arising in mathematical physics.