Gravitational Field of Fractal Distribution of Particles

Abstract

In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of the Gauss's law, we consider the simple examples of the fields of homogeneous fractal distribution. The examples of gravitational moments for fractal distribution are considered.

14 pages, LaTeX

References in corpus (10)

• Continuous Medium Model for Fractal Media
• Fractional Ginzburg-Landau equation for fractal media
• Fractional Hydrodynamic Equations for Fractal Media
• Fractional Generalization of Gradient and Hamiltonian Systems
• Fractional Generalization of Liouville Equations
• Fractional Systems and Fractional Bogoliubov Hierarchy Equations
• Fractional Liouville and BBGKI Equations
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• Review of Some Promising Fractional Physical Models
• Continuous Limit of Discrete Systems with Long-Range Interaction
• Vector Calculus in Non-Integer Dimensional Space and its Applications to Fractal Media
• Anisotropic Fractal Media by Vector Calculus in Non-Integer Dimensional Space
• Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• Fractional Derivative as Fractional Power of Derivative
• Nonholonomic Constraints with Fractional Derivatives
• Magnetohydrodynamics of Fractal Media
• Psi-Series Solution of Fractional Ginzburg-Landau Equation
• Symmetry Analysis of Initial and Boundary Value Problems for Fractional Differential Equations in Caputo sense
• Solutions of a particle with fractional $\delta$-potential in a fractional dimensional space
• Liouville and Bogoliubov Equations with Fractional Derivatives
• 1/r potential in higher dimensions
• Saturn rings: fractal structure and random field model
• Fractional Reduced Differential Transform Method for Belousov-Zhabotinsky reaction model