Abstract

AbstractFor the first time, this chapter analyzes the evolution stages of an unblown bud (plumeria) while monitoring the temporal evolution by measuring the behavioral variations in the complex impedance. Owing to their overabundance in tropical and subtropical areas and the superior medicinal and aromatic values of plumeria flowers of the Apocynaceae family have attracted much attention to studying the structures of their chemical constituents at the molecular level to evaluate their pharmaceutical efficacies. While minimizing the toxic effects of the drug on less selective targets and identifying better selective pathways, an in-depth analysis of their structures facilitates the identification of biological activities at the molecular level, which can be extended further to proliferate the medicinal applications in the form of molecular medicine.The analyses carried out in this chapter demonstrate that seemingly nondeterministic quasi-chaotic variations in measured complex impedance can be accurately (with fitting error less than 0.25%) modelled, by the proposed fitting formula with new fractal elements having complex conjugated power law of exponents. While studying the impedance characteristics of plumeria bud to identify the sequential stages of the transfer of charge phenomena, the stages of temporal evolution are identified through modeling of existing conducting channels forming 3D heterogenous branching structure in the intermediate range of frequencies.Besides, the proposed model implies that a new fractal element with complex conjugated power-law exponents really exists in nature and can be discovered in many biological systems. Earlier, we found a similar behavior in a randomly taken basil leaf, representing itself an example of 2D branching/fractal system. The detection of a new fractal element in living systems undoubtedly enriches the existing theory of the fractional calculus and opens a new direction of its research associated with biological systems.Keywords3D branching/fractal systemsImpedance measurements in unblown bud flower (Frangipani plumeria)New fractal element with complex-conjugated power-law exponents in living systems

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