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this paper studies the perturbed klein-gordon equation by the aid of several methods of integrability. there are six forms of nonlinearity that are considered in this paper. the parameter domains are thus identified.

The linear dielectric response of an assembly of noninteracting symmetrical top molecules (each of which is free to rotate in space) is evaluated in the context of fractional dynamics. The infinite hierarchy of differential-recurrence relations for the relaxation functions appropriate to the dielectric response is derived by using the underlying inertial fractional Klein-Kramers equation. On so...

The fractional Klein-Kramers (Fokker-Planck) equation describing the fractal time dynamics of an assembly of fixed axis dipoles rotating in an N-fold cosine potential representing the internal field due to neighboring molecules is solved using matrix continued fractions. The result can be considered as a generalization of the solution for the normal Brownian motion in a cosine periodic potentia...

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...

Graphene is a monoatomic layer of graphite with Carbon atoms arranged in a two dimensional honeycomb lattice configuration. It has been known for more than sixty years that the electronic structure of graphene can be modelled by two-dimensional massless relativistic fermions. This property gives rise to numerous applications, both in applied sciences and in theoretical physics. Electronic circu...