Fractal Dimension (Df) of Ismail’s Fourth Entropy (HIV⁽q,a1, a2,..,ak⁾) with Fractal Applications to Algorithms, Haptics, and Transportation

The current paper provides my fourth entropic formula, Ismail’s fourth entropy, namely $(H_{IV}^{(q,a_{1},a_{2},..,a_{k})})$, which is a novel generalization to Shannonian entropy with a visionary link to both long- and short-range interactions, (LRIs), (SRIs) respectively. The fractal dimension of $H_{I}^{(\gamma,q,a,b)}$ is identified in this paper. Following this, some potential fractal applications to algorithms, haptics, and transportation are highlighted. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.