Exact Solutions to Some Conformable Time Fractional Equations in Benjamin-Bona-Mahony Family

Abstract: The conformable time fractional forms of some partial differential equations are solved in the study. The existence of chain rule and the derivative of composite function enable the equations to be reduced to some ordinary differential equations by using some particular wave transformations. The modified Kudryashov method implemented to derive the exact solutions for the Benjamin-Bona Mahony (BBM), the symmetric BBM and the equal width (EW) equations in the conformable fractional time derivative forms. The obtained explicit solutions are illustrated for some time fractional orders in the interval $(0,1]$.