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Cancer is the world’s second-biggest cause of death, accounting for roughly 10 million deaths in 2020 and estimated to reach 16 million by 2040. In this study, we propose a novel technique for the treatment of tumor models with a power-law kernel with the Sumudu transform. The analysis was made for a generalized form of analytical solution that is unique and Picard K-stable by using Hilbert and Banach space results. The model investigates the Ulam-Hyers-Rassias stability, uniqueness of solutions, and impact of fractional derivatives with the power-law kernel. Reproductive number analysis with an equilibrium point shows the bounded solution in the feasible region. In the end, numerical simulations are drawn through figures at different fractional and fractal dimensions for the dynamics of treatment and the growth of normal cells. The analysis shows crucial criteria for system stability, ensuring the efficacy of therapeutic interventions through novel mathematical and biological insights. [ABSTRACT FROM AUTHOR]

Genetics, birth defects, some viral diseases, persistent ear infections, medications, loud noises, and age can all cause hearing loss, a global health issue. The mumps are typically the cause of unilaterally acquired sensorineural hearing loss in children. A hybrid fractional operator model employing Constant Proportional Caputo (CPC), Constant Proportional Caputo Fabrizio (CPCF), and Constant Proportional Atangana-Baleanu Caputo (CPABC) in the Caputo sense is developed to investigate mumps induced hearing loss in children. We focused on the region that is positively invariant and well-posed in the suggested model. We assessed the endemic and disease free equilibrium, reproductive number, strength number, and parameter sensitivity, and examined the global stability of the proposed system. The existence, uniqueness, and Hilfer generalized proportional operators for the constant of proportionality of the system’s solutions are demonstrated using fixed-point theorems. We simulated a system of fractional differential equations analytically using the Laplace Adomian Decomposition Method (LADM). This study is important since it is the first to model mumps related hearing loss using a fractional order model based on hybrid fractional operators without a singular kernel. The fractional-order derivative retains the system memory effect, is nonlocal, and outperforms the integer-order derivative in this regard. This sort of study aids medical professionals in diagnosis, treatment planning, and decision-making for mumps induced hearing loss. [ABSTRACT FROM AUTHOR]

Using the power of numerical computation through Levenberg Marquardt backpropagation ($LMB$LMB), the fluidic issue in the present study has features of heat transfer by convection in the hybrid nanofluid suspension of magnesium oxide and gold nanoparticles. The influence of slip effects on boundary layer flow with viscous dissipation at the nodal/saddle stagnation point is examined using a mathematical model. The current study considers water to be the base fluid, $MgO$MgO and $Au$Au as nanoparticles, and the circular cylinder to be the medium’s surface. Non-linear partial differential equations are converted into ordinary differential equations via similarity transformations. The dataset for Levenberg Marquardt backpropagation is generated in Mathematica software using an explicit RK-4 approach by varying different parameters such as the slip parameter ($\lambda $λ), convective parameter ($Bi$Bi), Eckert number ($E{c^*}$Ec∗) and volume fraction (${\phi _2}$ϕ2), Bi with Ec. Validation, training, and testing are utilized for network modeling through the Levenberg-Marquardt backpropagation approach for various scenarios of the fluidic model. The result shows that the base fluid’s thermal behavior is quickly increased by the $MgO - Au$MgO−Au/water hybrid nanofluid. The reliability of the findings is evaluated using autocorrelation, regression, mean square error, absolute error, and error histogram analyses. [ABSTRACT FROM AUTHOR]