By Muhammad Zubair, Muhammad Junaid Mughal, Qaisar Abbas Naqvi
This publication offers the idea that of fractional dimensional house utilized to using electromagnetic fields and waves. It presents demonstrates the benefits in learning the habit of electromagnetic fields and waves in fractal media.
The ebook offers novel fractional house generalization of the differential electromagnetic equations is equipped in addition to a brand new type of vector differential operators is formulated in fractional area. utilizing those converted vector differential operators, the classical Maxwell's electromagnetic equations are labored out. The Laplace's, Poisson's and Helmholtz's equations in fractional area are derived by utilizing converted vector differential operators.
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Additional info for Electromagnetic Fields and Waves in Fractional Dimensional Space
Then for E to be normal to H and zˆ , E must have an xˆ component. 1 General Plane Wave Solutions in Fractional Space: Lossless Medium Case 33 Fig. 5). [This figure was originally published in  , reproduced courtesy of The Electromagnetics Academy] where, η0 is wave impedance in free space. Assuming a time dependency e jwt and Js0 = −2 A/m, the solution for the usual wave for z > 0 with D = 3 is shown in Fig. 1, which is comparable to well known plane wave solutions in 3-dimensional space .
13) This equation is known as Poisson’s equation in fractional space. 15) where, r is the distance from any point on charge density to observation point. 15). 17). 19) where, R is the distance between any point in the source to observation point, Γ (x) (2) is the gamma function and Hn (kR) denotes the Hankel function of second kind of order n representing outward waves from source point. 19). For D = 3, we have n = −1/2. 21) where, C is a constant term. 21) is in exact agreement with the solution provided in  for Euclidean space.
In Sect. 2, time-varying auxiliary potential is studied in fractional space. 1 Electrostatic Potential in Fractional Space In this section, an exact solution of the Laplace’s equation for electrostatic potential in D-dimensional fractional space is presented. As an application, the electrostatic potential inside the rectangular box with surfaces held at constant potentials is obtained in fractional pace. It is also shown that for integer value of dimension D, the classical results are recovered.
Electromagnetic Fields and Waves in Fractional Dimensional Space by Muhammad Zubair, Muhammad Junaid Mughal, Qaisar Abbas Naqvi