Invariance properties and conservation laws of perturbed fractional wave equation

In this research, the group formalism, invariance properties and conservation laws of the nonlinear perturbed fractional wave equation have been explored. The method used in this paper was first described by Lukashchuk (Commun Nonlinear Sci Numer Simul 68:147-159, 2019). He shows that when the order of fractional derivative in a fractional differential equation is nearly integers, it can be approximated to a perturbed integer-order differential equation with a small perturbation parameter. Perturbed and unperturbed symmetries are found, and some new solutions are computed by the symmetry operators of the equation. These solutions are obtained by the invariant transformations of the symmetries. Also one-dimensional optimal system is used to derive another exact solutions. Finally, the nonlinear self-adjointness concept is applied in order to find conservation laws with informal Lagrangians.