Clinical Applications of Fractals and Fractional Order Systems | Book Publisher International

 Fractional calculus as a generalization of integer-order calculus has been used widely in biology, physics, and finance. The major advantage of fractional-order to integer-order operators is their ability to reveal the complicated dynamics of given systems which makes them a more realistic framework to model different biological and physical phenomena. While the integer-order models provide a small class of non-integer order models, using fractional order operators, we can study different classes of the same model by changing the fractional-order. Therefore, these models provide us more flexibility to analyze and control the behavior of a system. During recent decades many efforts in the area of fractal geometry have been made to discover and control the nonlinear and complicated dynamics of different systems that exhibit fractal processes. A fractal has been defined as a subset of Euclidean space with a dimension strictly higher than its topological dimension. For the first time, Mandelbrot in 1983 introduced these irregular geometric objects to the world. Fractals also can be defined as physical models for different phenomena which are distributed evenly in the embedding space. Fractals are well-known because of their unique property which is self-similarity in different scales. During recent decades, researchers in different field of sciences have developed varieties of interesting studies about the unique properties of fractals.

Author(s) Details:

Tahmineh Azizi,
Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin-Madison, USA.

Please see the link here: https://stm.bookpi.org/CAFFOS/article/view/9926

Vortex Diffractal in Free Space | Chapter 6 | Fundamental Research and Application of Physical Science Vol. 1

 Brief information data on the properties of light beams accompanying a fractal structure (diffractals) are likely. New information about the propagation of diffractals in emptiness was also found. Particular attention was paid to the characteristics of vortex diffractals. The research established two-dimensional Weierstrass functions and specific forms of Gaussian beams was carried out. The acted analysis indicated a extreme information capacity of whirlpool diffractals and explained their opposition to the turbulence in the propagation medium. It was raise that the morphology of their transverse size-phase distribution remnants unchanged all the while the propagation. The obtained results will suffice in the development of ocular information systems established fractal vortex beams.

Author(s) Details:

Korolenko Pavel Vasil'evich,
Faculty of Physics, Lomonosov Moscow State University, Russia.

Zotov Alexei Mikhailovich,
Faculty of Physics, Lomonosov Moscow State University, Russia.

Kubanov Rustam Tatarhanovich,
Faculty of Physics, Lomonosov Moscow State University, Russia.

Pavlov Nikolai Nikolaevich,
Faculty of Physics, Lomonosov Moscow State University, Russia.

Please see the link here: https://stm.bookpi.org/FRAPS-V1/article/view/9975

Study about Fractals Dynamics and Designs| Chapter 3 | Current Overview on Science and Technology Research Vol. 2

 The strong yet unnoticed field of fractals is concentrated on here by the creator alongside its set of experiences and past applications. Fractal elements and configuration is a complete high level branch which helps in the investigation of self-association in nature as well as shows a fluctuated applications. Creator here likewise attempted to create and work out the surface region of an imperceptibly developing fractal with its overall articulation. The endless surface region limited in noticeably limited district is the striking property of a fractal which can be utilized to make sense of even the presence of dark openings might be in future. The proposed section is to expand another fractal planned with its particulars and to propose a reasonable record which might require hypothetical and useful confirmations later on.

Author(s) Details:

Bhakti Parag Rajvaidya,
G H Raisoni College of Engineering, Nagpur, India.

Please see the link here: https://stm.bookpi.org/COSTR-V2/article/view/7985