The Fractal Dimension Theory of Ismail's Third Entropy with Fractal Applications to CubeSat Technologies and Education
Keywords:
Fractal dimension (Df), Ismail's third entropy, CubeSat technologies, EducationAbstract
As a mathematical concept, entropy is the first and most advanced of its kind. Only a handful of studies have examined the fractal dimensions of fundamental entropies, including Shannon, Tsallis, and Rényi entropic expressions, in the literature. This served as a deliberative source of inspiration for further investigation into the direction of a cohesive information-theoretic fractal theory. The current study begins with introducing my third entropy formula, which is Ismail's entropy, or ( ) as a novel generalisation to Shannonian entropy with a forward-thinking connection to both long- and short-range interactions, or SRIs and LRIs, respectively. This would obviously lead to a fourfold unification with modern physics and statistical mechanics. This gives the study greater validity and weight. This study determines the fractal dimension of . This study played a significant role in drawing attention to the value of fractal geometry for the space industry and education, both of which are vital for advancing our civilizations. Consequently, a few possible fractal applications to education and CubeSat technologies are emphasized. Thus, the extensive hunt for additional ground-breaking research has concluded. Of course not this served as another motivation for me to suggest fresh, open challenges that would allow the scientific community to explore more avenues for research. Lastly, a combined overview is given with thought-provoking research topics and the next study stage.
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