In this paper, we establish a new iterative process for approximation of fixed points for contraction mappings in closed, convex metric space. We conclude that our iterative method is more accurate and has very fast results from previous remarkable iteration methods like Picard-S, Thakur new, Vatan Two-step and K-iterative process for contraction. Stability of our iteration method and data dependent results for contraction mappings are exact, correspondingly on testing our iterative method is advanced. Finally, we prove enquiring results for some weak and strong convergence theorems of a sequence which is generated from a new iterative method, Suzuki generalized non-expansive mappings with condition $(C)$ in uniform convexity of metric space. Our results are addition, enlargement over and above generalization for some well-known conclusions with literature for theory of fixed point.

We investigated the combined impact of convective boundary conditions, thermal conductivity, and magnetohydrodynamic on the flow of a tangent hyperbolic nanofluid across the stratified surface. Furthermore, the ramifications of Brownian motion, thermophoresis, and activation energy were considered. Heat generation, chemical reactions, mixed convection, thermal conductivity, and other elements were considered when analyzing heat transfer phenomena. The governing equations were converted via similarity transformations into non-dimensional ordinary differential equations in order to analyze the system. Using the shooting method, the problem's solution was determined. We showed the mathematical significance of the temperature, concentration profiles, and velocity of each fluid parameter. These profiles were thoroughly described and shown graphically. The findings demonstrated that as the Weissenberg number and magnetic number increased, the fluid velocity profile decreased. Higher heat generation and thermophoresis parameters resulted in an increase in the temperature profile. Higher Brownian motion and Schmidt parameter values resulted in a drop in the concentration profile. Tables were used to discuss the numerical values of skin friction ( $C_{fx}$), Nusselt number ( ${Nu}_x$), and Sherwood number ( $S{h}_x$). For the greater values of Weissenberg number and mixed convection parameters, skin friction numerical values fell while Nusselt numbers rose.

Mathematical formulations are crucial in understanding the dynamics of disease spread within a community. The objective of this research is to investigate the SEIR model of SARS-COVID-19 (C-19) with the inclusion of vaccinated effects for low immune individuals. A mathematical model is developed by incorporating vaccination individuals based on a proposed hypothesis. The fractal-fractional operator (FFO) is then used to convert this model into a fractional order. The newly developed SEVIR system is examined in both a qualitative and quantitative manner to determine its stable state. The boundedness and uniqueness of the model are examined to ensure reliable findings, which are essential properties of epidemic models. The global derivative is demonstrated to verify the positivity with linear growth and Lipschitz conditions for the rate of effects in each sub-compartment. The system is investigated for global stability using Lyapunov first derivative functions to assess the overall impact of vaccination. In fractal-fractional operators, fractal represents the dimensions of the spread of the disease, and fractional represents the fractional ordered derivative operator. We use combine operators to see real behavior of spread as well as control of COVID-19 with different dimensions and continuous monitoring. Simulations are conducted to observe the symptomatic and asymptomatic effects of the corona virus disease with vaccinated measures for low immune individuals, providing insights into the actual behavior of the disease control under vaccination effects. Such investigations are valuable for understanding the spread of the virus and developing effective control strategies based on justified outcomes.