## 1 Introduction  
The development of eco-friendly nanomaterials using agro-industrial waste has progressed significantly due to the environmental concerns linked with chemically synthesizednanomaterials [1]. Agro-industrial waste utilization enables resource vaporization and reduces waste disposal costs. This study introduces bird eggshells as a calcium precursor for synthesizing hydroxyapatite through a combined microwave-ultrasonic method [2]. Currently, eggs are widely utilized as food additives, generating around 250,000 tons of eggshell waste annually [3]. Although biodegradable, eggshells require four to six weeks to decompose completely, often emitting unpleasant odors and carrying pathogens like _Salmonella_[4]. Recently, interest has grown in employing eggshell waste for chemical synthesis, particularly as a precursor for hydroxyapatite Ca\({}_{10}\)(PO\({}_{4}\))\({}_{6}\)(OH)\({}_{2}\) (Hap) through hydrothermal and sol-gel methods [5]. This approach yields a material with superior resistance and crystallinity compared to that derived from 4H\({}_{2}\)O-Ca(NO\({}_{3}\))\({}_{2}\)[6], showing promise as a nanofertilizer (supplying nutrients like Ni, Ca, P, and K) and as a phytohormone carrier [7]. As a bioceramic, Hap is rich in calcium and phosphorus, promoting plant growth due to its nutrient availability, non-toxicity, and biocompatibility. Phytohormones further stimulate gibberell receptors for stem and root elongation and auxin receptors for fruit growth. Forchlorfenuron (FCF) is an effective growth-regulating hormone that enhances cell division, leading to increased fruit size and synergistic action with auxins and gibberellins, thus promoting more pronounced lateral growth than traditional growth methods [8; 9]. According to [PERSON] et al., phytohormones at concentrations of 5% or lower pose no health risk to consumers [10]. Moreover, advanced technologies such as simultaneous microwave-ultrasonic (MO-US) applications in Hap synthesis offer reduced synthesis times (from hours to minutes) and precise control over texture and morphology, dependent on irradiation time and power. It is noteworthy that the MO-US method has not yet been reported. While the MO-US method offers significant advantages, it is important to note that it also carries potential risks, such as forming reactive species that could be harmful if not properly managed. Microwave irradiation aligns molecular dipoles with electric and/or magnetic fields, inducing molecular movement and dipole rotation, leading to overheating and forming reactive species (free radicals, anions, and cations) that catalyze reactions quickly [11]. Ultrasonic irradiation generates high pressures and temperatures at localized points within a solution, caused by the formation, expansion, and implosion of bubbles (cavitation) due to ultrasonic wave expansion and compression in the liquid medium, producing reactive species that drive chemical reactions [11; 12]. This research proposes a high-potential hydroxyapatite fertilizer synthesized using MO-US and loaded with forchlorfenuron (Hap-FCF) in suspension, allowing soil mobility and root penetration via the mass flow of water due to transpiration. This increases the availability of phosphorus, calcium, and forchlorfenuron to plants, preventing soil fixation and reducing fertilizer requirements. Such approaches foster sustainable and environmentally friendly agriculture by minimizing input needs and nutrient loss [1]. Growth stimulators offer high biocompatibility and biodegradability; their biological profile ensures the safety of human and environmental health when applied in open fields. In silico methods are increasingly used to predict and validate experimental techniques, assess interactions between organic molecules and biological proteins, and identify stable conformations and potential interaction sites [13]. In contrast, molecular prediction tools have been extensively applied in the pharmaceutical industry to identify new biological targets.