Lie symmetries, exact solutions, and conservation laws of the nonlinear time-fractional Benjamin-Ono equation

In this work, we use the symmetry of the Lie group analysis as one of the powerful tools which that deals with the wide class of fractional order differential equation in the Riemann-Liouville concept. We employ the classical Lie symmetries to obtain similarity reductions of nonlinear time-fractional Benjamin-Ono equation and then, we find the related exact solutions for the derived generators. Finally, according to the Lie symmetry generators obtained, we construct conservation laws for related classical vector fields of time-fractional Benjamin-Ono equation.