**1. Introduction**

According to the Drug and Lactation Database, "Melatonin is the hormone produced by the pineal gland that plays a role in regulating sleep and circadian rhythm as well as a possible role in gut-brain signaling*.*" As it is stated in the Drug and Lactation Database, melatonin (methoxyindole) is used for the organization of the circadian rhythms, especially core temperature and sleep–wake rhythms [1]. Melatonin is also characterized as a full-service anticancer agent due to its functions: inhibition of initiation, progression, and metastasis phases of tumors [2]. Aside from its antioxidant, anticancer, antitumor, anti-inflammatory, antiaging, antidiabetic, antiviral, and neuroprotective activities, melatonin exhibits a therapeutic potential in the treatment of asthma, respiratory diseases or infections, chronic obstructive pulmonary disease, lung cancer, pleural cavity diseases, as well

as vascular pulmonary diseases [3]. Melatonin is also used as a food supplement and nutraceutical. The dosage and release profile of melatonin are very crucial factors that affect the effectiveness of treatment, especially in older adults [4]. According to a recent critical analysis, in older adults, the use of the lowest possible dose of immediate-release formulation of melatonin is appropriate to best mimic the normal physiological circadian rhythm of melatonin and to avoid prolonged, supraphysiological blood levels [4].

Melatonin has been encapsulated in different conventional and nanotechnological systems [5]. In the majority of the cases, the aim of the incorporation of melatonin into formulations is to achieve controlled or sustained release. The aim of this chapter is to present the conventional solid and liquid forms (i.e., tables, emulsions, suspensions, etc.) and the nanoformulations of melatonin and to give special attention to release kinetics from the pharmaceutical vehicle.

Furthermore, fractal analysis is a mathematical tool to quantify nature and physical systems' complexity [6]. Fractals have been observed in powdered drug substances, in excipients, and in their mixtures, as well as in semifluid dosage forms like gels and emulsions [6]. Fractals have been used to describe the dimensions of dosage forms, such as tablets, matrix tablets, and spheres [6]. The application of fractal geometry for the quantification of the dimensionality of advanced drug delivery nanosystems (aDDnS) recently appeared in the literature [5, 6]. For example, liposomes, micelles, polymersomes, and other nanosystems are fractal objects [6]. Additionally, the fractal and fractional kinetics can model very close to the reality the release of drugs from polymeric matrices and other dosage forms, both solid and liquid [7–9].

In this chapter, we are going to find the interrelationship between the fractal dimension of pharmaceutical vehicle and the release profile of melatonin. Several examples will be given in order to understand in depth the reason of controlledrelease profile of melatonin and its added value for the development of a new medicine and/or nutraceutical.
