TY  - EJOU
AU  - Ghannam, Manal 
AU  - Kaymakamzade, Bilgen 
AU  - Farman, Muhammad 
AU  - Nisar, Kottakkaran Sooppy 
AU  - Ahmed, Mohammed Altaf 

TI  - Fractional Order <i>In Vitro</i> Fertilization Model Real Data Analysis with Novel Application of Inequalities via Stability and Computational Techniques
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2026
VL  - 148
IS  - 1
SN  - 1526-1506

AB  - <i>In Vitro</i> Fertilization (IVF) has been a major medical advancement in the field of fertility treatment. It has helped millions of individuals and couples overcome infertility by providing a workable option. It involves removing eggs from the ovaries of a female, fertilizing those eggs with male sperm in a monitored lab condition. In this work, we developed a new model to show the success of <i>In Vitro</i> Fertilization rates in women through a fractional-order compartmental modeling framework by using real data. The developed model is analyzed statistically, and the biological feasibility of the model. The Lipschitz condition, expressed by the Lipschitz inequality, suggests that the change in a function’s output is limited by a constant known as the Lipschitz constant in relation to the input changes between any two points in its domain. This characteristic ensures that solution routes remain consistent, resulting in well-behaved and singular solutions. The linear growth inequality describes the condition of linear growth by asserting that one variable can be limited by another that rises linearly. This inequality is crucial because it prevents differential equation solutions from rising too rapidly, ensuring that they remain within established boundaries. We used Volterra integral inequality with a Volterra-type Lyapunov function to analyze the fractional derivatives of Lyapunov functions in a fractional-order system, which is necessary to establish global asymptotic stability. This extends the standard Lyapunov stability theory to fractional-order systems, particularly in the analysis of complex models like the infectious disease model, by providing a method to constrain the behavior of the system without solving the differential equations explicitly. Additionally, a sensitivity analysis of several aspects is derived through mathematical simulations. Additionally, we use numerical simulations to validate our theoretical findings at different fractional orders.
KW  - <i>In vitro</i> fertilization; fertile oocyte donors; health care; volterra type inequality; lipschitz inequality; caputo operator

DO  - 10.32604/cmes.2026.081075