This paper studies the Klein-Gordon equation and two modifications in an infinite Cantor set a fractal space-time. Their variational formulations are established discussed, spatio-temporal discontinuity requires both spatio-fractal derivative temporal for practical applications. Some basic properties of local fractional two-scale elucidated, derivation Euler-Lagrange is illustrated.

Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We...

In this paper, we consider the Cauchy problem for Klein-Gordon equation with a cubic convolution nonlinearity in R. Making use of Bourgain’s method in conjunction with precise Strichartz estimates of S.Klainerman and D.Tataru, we establish the Hs-global well-posedness with s < 1 of the Cauchy problem for the cubic convolution defocusing Klein-Gordon-Hartree equation, inspired by I. Gallagher an...

Abstract In [1] Varsha and Jaferi proposed an iterative method for solving nonlinear functional equations, viz. nonlinear Voltera integral equations, algebraic equations and system of ordinary differential equations. Then Sachin and Varsha [2] implemented this method to solve linear and nonlinear partial differential equations of integer and fractional order. The aim of this article is to propo...

We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schrödinger, Klein–Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in t...