https://doi.org/10.1140/epjp/s13360-021-01595-6
Regular Article
Invariance properties and conservation laws of perturbed fractional wave equation
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
Received:
28
February
2021
Accepted:
21
May
2021
Published online:
2
June
2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
