Abstract
Abstract In this paper, the local fractional variational iteration method is given to handle the damped wave equation and dissipative wave equation in fractal strings. The approximation solutions show that the methodology of local fractional variational iteration method is an efficient and simple tool for solving mathematical problems arising in fractal wave motions. MSC:74H10, 35L05, 28A80.
Highlights
The variational iteration method was effectively applied in various fields of science and engineering [ – ] and the references therein
It is in some cases, more powerful than the existing techniques, e.g., the fractional variational iteration method [, ], the homotopy perturbation method [, ], the exp-function method [, ], the decomposition method [ – ], the homotopy analysis method [, ] and others [ ]
The purpose of this paper is to present the solutions of the damped wave equation and the dissipative wave equation in fractal strings equipped with fractal initial conditions
Summary
The variational iteration method was effectively applied in various fields of science and engineering [ – ] and the references therein. The fractal time-space structure for dealing with the non-differentiability and infinities of fractals derived from local fractional operators was presented in [ – ] and the references therein. We consider a general wave equation of a fractal string within the local fractional operators, namely. Lξ( ξα)u(ζ , ξ ) = Lt(t α)u(x, t), Rξ(α)u(ζ , ξ ) = –Lt(α)u(x, t), g(ζ , ξ ) = Lx( xα)u(x, t) + Lx(α)u(x, t) + m(x, t), and we have the following dissipative wave equation in fractal time space: Lt(t α)u(x, t) – Lt(α)u(x, t) – Lx( xα)u(x, t) – Lx(α)u(x, t) – m(x, t) = , ≤ x ≤ l, t > , ( ). The local fractional variational iteration method, which was structured in [ ], was applied to solve heat conduction equation on Cantor sets [ ] and the local fractional Laplace equation [ ].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
