Lalbhai Dalpatbhai College of Engineering

Mathematical epidemic models increasingly incorporate fractional calculus to better capture memory effects and heterogeneous transmission dynamics. In this study, we formulate a conformable fractional SEIR model incorporating vaccination as a time-dependent control strategy. Unlike classical integer-order formulations, the conformable derivative introduces temporal memory behavior without losing essential differential properties. Stability analysis of the disease-free equilibrium demonstrates that vaccination intensity significantly contributes to reducing the effective reproduction number. A modified fractional Runge–Kutta numerical method is developed and implemented to approximate solutions with improved stability and accuracy over traditional schemes. Numerical simulations demonstrate how the fractional order and vaccination rate jointly govern epidemic peaks, persistence, and eradication timelines. The results confirm that fractional dynamics and adaptive vaccination policies yield more realistic epidemic trajectories than classical models. The proposed framework provides an efficient tool for assessing public-health vaccination strategies under memory-dependent epidemic evolution.

Metamaterial absorbers (MMA) have emerged as viable options for electromagnetic wave manipulation owing to their compact design, tunability, and high absorption efficiency. This work presents the design and analysis of a switchable MMA that incorporates vanadium dioxide (VO2) to achieve thermally tunable absorption characteristics. The structure consists of a polyimide layer serving as the dielectric substrate, a gold-based ground plane, and a top surface of VO2. This designed MMA produces a 9.7 THz bandwidth by keeping absorption levels over 92% in the 4.5-14.2 THz band with a fractional bandwidth (FBW) of 103.74%. The absorption peak consistently rises from 2% to 99.3% with changes in conductivity of VO2 from 200 to 2 & times; 105 S/m. This changeover allows thermal tunability between highly reflecting and extremely absorbent phases. In order to analyze the absorption response of the proposed MMA, many dielectric layers are considered, including polyimide, lossy silicon, Al2O3, Quartz lossy, and SiO2. Additionally, the absorption response of the MMA is also evaluated using various conductive materials (aluminium, gold, copper, iron) apart from VO2. An analysis on the effects of incidence and polarization angles on absorbance in TE and TM modes is performed in order to confirm the polarization insensitivity of the designed MMA. The suggested MMA has a wide range of possible terahertz-based uses, including biosensing, medical imaging, cloaking, EMC and optical switches.

Solar energy generation and its research have improved a lot in the past decade. Solar energy generation and its efficiency have improved by using different optical techniques and materials to improve it. Solar absorbers are one of the important parts of solar energy generation, as they generate heat energy from solar radiation. The heat generated through solar absorbers is renewable in nature and environmentally friendly. Our research on a solar structure composed of MXene-MgF2-MXene, intended to enhance the absorption of solar energy. This configuration involved graphene material to improve the efficiency of the overall structure. In the current research, a radiated energy of 93.47% is achieved over the solar spectral region consists of UV, Visible, and Near infrared regions. Machine learning optimization is used to increase the efficiency of the solar absorber. The newly researched absorber, designed for thermal energy systems, holds major promise for a wide array of applications in both heating and cooling processes. This advanced absorber can be effectively utilized across numerous sectors, including agriculture, where it can optimize temperature control for crops and greenhouses, as well as in industrial settings, where it can contribute to more efficient energy use in manufacturing and processing environments. Additionally, it offers promising applications in residential and home settings, providing a sustainable solution for space heating and cooling.

Solar energy is essential for driving the transition toward a clean and sustainable energy cycle. Research on solar absorbers is a key focus in solar energy systems, as it directly contributes to improved energy harvesting performance. The current design with the material composition of the Cr-Fe3O4-ZrO2 and a graphene nanostructure is applied in the investigation of the current solar structure. The current absorber can work in the ultra-wideband (UV-MIR) spectra and with an efficient rate of 94.66% for 2800 nm. Moreover, the current solar absorber can reach 97.38% for 1000 nm with the proficient square-resonator design. We distributed the machine learning section in the current work to describe the predicted and actual value output in each parameter with the linear regression method. With the good efficiency of radiation, the current research can be used as a renewable energy option in hatcheries and dairies, swimming pool warming, the agricultural sector, health clubs, boiler feed, and so on.

Based on the surface plasmon resonance (SPR) technique, the proposed biosensor is investigated as an SPR-based sensing platform for detecting breast cancer cells, specifically MCF-7 and MDA-MB-231 cells. Developed biosensor features an octagonal cylinder-shaped resonator design composed of two novel materials: an octagon-shaped structure made of gold (Au) and a cylinder-shaped structure made of silver (Ag). Graphene is also integrated to achieve high sensitivity in the detection for the two breast cancer cell lines based on the refractive index values, within the wavelength range of 1650-1700 nm, yielding sensitivity rates of 714.28 nm/RIU (MCF-7) and 785.71 nm/RIU (MDA-MB-231). The proposed Graphene Octagonal Cylinder-Shaped Surface Plasmon Resonance (GOCSPR) biosensor consists of two layers, with a ceramic substrate made of aluminum nitride (AlN), and exhibits good quality factors of 560 for MCF-7 and 557 for MDA-MB-231. The analysis of layer height and cylinder radius, along with optimization using a Linear Regression machine learning algorithm and the corresponding R2 values, is also presented in the manuscript. The designed graphene-based structure can be used for detecting breast cancer cell with high efficiency for medical applications.