About Maxwell’s equations on fractal subsets of ℝ3

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Alireza Golmankhaneh ◽  
Ali Golmankhaneh ◽  
Dumitru Baleanu

AbstractIn this paper we have generalized $$F^{\bar \xi }$$-calculus for fractals embedding in ℝ3. $$F^{\bar \xi }$$-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. $$F^{\bar \xi }$$-fractional differential form is introduced such that it can help us to derive the physical equation. Furthermore, using the $$F^{\bar \xi }$$-fractional differential form of Maxwell’s equations on fractals has been suggested.

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Zhao ◽  
Dumitru Baleanu ◽  
Carlo Cattani ◽  
De-Fu Cheng ◽  
Xiao-Jun Yang

Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Local fractional differential forms of Maxwell’s equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell's equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell’s equations for the dynamics of cold dark matter.


Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 958 ◽  
Author(s):  
Sinan Deniz ◽  
Ali Konuralp ◽  
Mnauel De la Sen

The newly constructed optimal perturbation iteration procedure with Laplace transform is applied to obtain the new approximate semi-analytical solutions of the fractional type of damped Burgers’ equation. The classical damped Burgers’ equation is remodeled to fractional differential form via the Atangana–Baleanu fractional derivatives described with the help of the Mittag–Leffler function. To display the efficiency of the proposed optimal perturbation iteration technique, an extended example is deeply analyzed.


1995 ◽  
Vol 43 (3) ◽  
pp. 647-654
Author(s):  
L.E. Garcia-Castillo ◽  
M. Salazar-Palma ◽  
T.K. Sarkar ◽  
R.S. Adve

PIERS Online ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Fethi Bin Muhammad Belgacem

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>


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