Exact Solutions and Conservation Laws of Time-Fractional Levi Equation

Abstract

Exact solutions were derived for a time-fractional Levi equation with Riemann–Liouville fractional derivative. The methods involve, first, the reduction of the time-fractional Levi equation to fractional ordinary differential equations with Erdélyi-Kober fractional differential operator with respect to point symmetry groups, and second, use of the invariant subspace to reduce the time-fractional Levi equation into a system of fractional ordinary differential equations, which were solved by the symmetry group method. The obtained explicit solutions have interesting analytic behaviors connected with blow-up and dispersion. The conservation laws generated by the point symmetries of the time-fractional Levi equation are shown via nonlinear self-adjointness method.