Fractional Methods in Signal Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (15 February 2024) | Viewed by 465

Special Issue Editors

Department of Theoretical Physics and Wave Processes, Volgograd State University, 400062 Volgograd, Russia
Interests: quantum information; visualization; turbulence; signal processing; computer simulation; interstellar medium; gas dynamics; galaxy dynamics; hydrodynamical instabilities; accretion processes; radar astronomy; fractal calculus
Institute of Mathematics and Information Technologies, Volgograd State University, 400062 Volgograd, Russia
Interests: fractal signal processing; signal processing in short-range tasks; radar and radio navigation

Special Issue Information

Dear Colleagues, 

Until very recently, there was a consensus in the scientific community that the book of nature was written in the language of differential equations of an integer order and since the derivative of an integer order is a locally defined operation, it fully complies with the requirements of the fundamental principle of modern physics; the principle of locality.

If we reverse this statement, then we can say that if the equation contains derivatives of non-integer order, which are constructed as fundamentally nonlocal procedures, then it is not fundamental but derived from some approximate description.

Although the locality paradigm has been issued a certificate of validity, it is possible that this certificate has a limited expiration date and is about to expire. News from the front, or more precisely, from the frontier of quantum physics, constantly reminds us that locality is not so simple.

However, since the description of the space–time evolution of quantum entanglement has not yet advanced very much and the equations of the fundamental nonlocal theory have not yet been written, any fractional differential equations in physics look pretentious and alien and are perceived with skepticism by the scientific community.

Moreover, they are also not yet sufficiently promoted. The experience of communicating with specialists who use the mathematical apparatus in their research shows that most of them are not even aware of the existence of fractional derivatives, and this is all the more surprising given that more than three centuries have passed since the formulation of the idea of ​​a fractional derivative.

In this regard, an important activity is not only the development of new concepts related to fractional calculus, but also the implementation of those already developed long ago. This approach is characteristic of innovation, and we expect in the near future the flowering of fractional analysis as a useful innovation that will change both fundamental and applied science and technology.

This may be evidenced by the fact that the apparatus of fractional differential analysis is already serving as a powerful tool for building new methods in the field of computer science. That is, if we go from the material world to the world of ideas, numbers, and algorithms, then we can note that fractional calculus is not connected here by such confusions as the paradigm of locality, and we can expect a more rapid advancement of ideas and methods of fractional calculus.

With this Special Issue on fractional methods in signal theory, we hope to foster innovation in this area by following our vision of the current scientific landscape and following the agenda we have summarized in the humble manifesto presented above.

It is with great pleasure that we invite you to take part in filling this issue with your original research and review papers in the field of fractional calculus applications. Potential applications include, but are not limited to the application of fractal calculus in the development of innovative:

  • algorithms;
  • numerical methods;
  • real-time computing techniques;
  • methods of image and sound processing;
  • pattern recognition techniques;
  • concepts in control theory;
  • approaches to mathematical modeling in engineering;
  • approaches and concepts in financial mathematics;
  • methods of analysis in mathematical linguistics;
  • models of computational fluid dynamics;
  • models and concepts in the mechanics of gravitating media and cosmology;
  • ways of developing the theory of differential, integral, and integro-differential equations with fractional derivatives and/or integrals.

Prof. Dr. Ilya Kovalenko
Prof. Dr. Vladimir Zakharchenko
Guest Editors

Manuscript Submission Information

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Keywords

  • theory of differential, integral and integro-differential equations with fractional derivatives and/or integrals
  • modeling
  • computational mathematics
  • real-time computing
  • artificial intelligence
  • computational engineering
  • control theory
  • financial mathematics
  • mathematical linguistics
  • fluid dynamics
  • astrophysics

Published Papers

There is no accepted submissions to this special issue at this moment.
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