About Maxwell’s equations on fractal subsets of ℝ3

Abstract

Abstract:In this paper we have generalized F ξ -calculus for fractals embedding in R 3 . F ξ -calculus is a fractional local derivative on fractals. It is an algorithm which may be used for computer programs and is more applicable than using measure theory. In this Calculus staircase functions for fractals has important role. F ξ -fractional differential form is introduced such that it can help us to derive the physical equation. Furthermore, using the F ξ -fractional differential form of Maxwell's equations on fractals has been suggested.

Non-local Integrals and Derivatives on Fractal Sets with Applications

“…The F α -calculus is generalized and applied in physics as a new and useful tool for modelling processes on the fractals. Newtonian mechanics and Schrödinger equation on the fractal sets and curves are given [15,16,17]. The gauge integral is utilized to generalized the F α -calculus for the unbound and singular function [18].…”

New Derivatives on the Fractal Subset of Real-Line

“…Using F α -calculus the Newton, Lagrange and Hamilton mechanics were built on fractal sets [18,19]. Also, Schrödinger's equation on a fractal curve was derived in [20][21][22]. Motivated by the above-mentioned interesting results, in this work, we define the non-local derivative on fractal sets.…”

About Schrödinger Equation on Fractals Curves Imbedding in R 3

“…The classical mechanics is derived without the need of the least-action principle using path-integral approach [22]. The calculus on the fractals has been studied in different methods like probabilistic approach method, sequence of discrete Laplacians, measure-theoretical method, time scale calculus [23].Riemann integration like method has been studied since that is useful and algorithmic [24][25][26][27][28][29].Using the calculus on fractals the Newtonian mechanics, Lagrange and Hamilton mechanics, and Maxwell equations has been generalized [30][31][32]. As a pursue theses research we generalized the quantum mechanics on fractals.…”