Modern Mathematical Theories in Electromagnetism: Fractals, Wavelets and Fractional Operators
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".
Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 5721
Special Issue Editor
Interests: fractional calculus; wavelet analysis; fractal geometry; applied functional analysis; dynamical systems; information theory; Shannon theory; antenna theory; image processing
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Both information and energy can continuously change forms without losing their essence. The information is taken for a “ride” on the wave, at the speed of light, to be decoded later by a receiver. The majority of real-world signals have to ride an electromagnetic wave at some stage in their journey. Unfortunately, this process cannot be entirely free because electromagnetic waves are subject to the laws of propagation and scattering. The effects of these laws on communication are often ignored by the classical signal analysis and processing. Thus, in recent years, there has been growing interest in the application of three new mathematical theories, i.e., fractal geometry, wavelet analysis and fractional calculus, in electromagnetic modelling. In particular, fractal sets have become extremely popular thanks to their flexibility in modelling for real-world applications. Likewise, wavelet analysis has become popular and important due mainly to several applications in numerous and widespread fields of electromagnetism (small antennas theory, scattering, etc.). In particular, electromagnetism has shown that the fractal-wavelet approach can shed some new light on several unsolved problems. Moreover, the generalized physics laws involving fractional derivatives give new models. In addition, in the study of Maxwell equations in fractal media the derivatives are necessarily of fractional order. As a result, fractional calculus is now a powerful tool for the study of electromagnetic problems whenever the medium is non-classical. All three modern theories show rather strikingly that contemporary mathematics is capable of providing ever more refined models for electromagnetic applications. In general, the combined choice of pre-fractal set, wavelet basis and definition of fractional derivative relies on technical requirements and the complexity of the electromagnetic problem. Of course, their application sheds new light on potential results in some mathematical fields (PDEs theory, complex geometry, etc.).
In this Special Issue, we invite and welcome review, expository, and original papers dealing with recent advances in the application of fractal geometry, wavelet analysis and fractional calculus in electromagnetism. From a more general point of view, we also invite all theoretical and practical investigations in physics and engineering focused on this topic.
The main topics of this Special Issue include (but are not limited to):
- Wavelet electromagnetism;
- Scattering;
- Fractal antennas;
- Fractional electromagnetism;
- Fractal-wavelet models and electromagnetic radiation;
- Fractional Laplacians in electromagnetism;
- Fractional PDEs in electromagnetism;
- Geometrical configuration in electromagnetic problems;
- Fractional calculus in remote sensing.
Dr. Emanuel Guariglia
Guest Editor
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.
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