LAUSR

Real-world phenomena often are modelled by the nonlinear fractional differential equations. In this work, a novel technique called the $$\exp \left( { - \phi \left( \varepsilon \right)} \right)$$exp-ϕε method is employed to find the exact solutions of nonlinear FDEs. Some well-known time-fractional differential equations in the context of conformable derivative, viz. the time-fractional modified Benjamin–Bona–Mahony (BBM) equation and the time-fractional Cahn–Hilliard (CH) equation are considered to test the usefulness of the method. The utility of the $$\exp \left( { - \phi \left( \varepsilon \right)} \right)$$exp-ϕε method in solving nonlinear FDEs is proved.