Invariant Subspace Method for Fractional Telegraph Equations

Abstract

In this thesis, we use the invariant subspace method to find the solu- tions of three classes of fractional telegraph equations, i.e., space-, time-, and space and time-fractional telegraph equations, in which fractional derivatives are consid- ered in the Caputo sense. In this method, we first classify all possible invariant subspaces with respect to the differential operator. By assuming the solution to be a linear combination of functions in the appropriate invariant subspace, the fractional telegraph equation is reduced to a system of fractional ordinary differential equa- tions. Finally, solving the system of fractional ordinary differential equations yields the solution of fractional telegraph equation.