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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]

In this article, we tackle the optimal control and controllability of neutral fractional nonlocal integro-differential equations (NFNIE) of Atangana–Baleanu–Caputo with non-instantaneous impulses. Semigroup theory, noncompactness measurements and fixed point approaches were used to attain the results. An illustration is provided to support the theoretical findings. [ABSTRACT FROM AUTHOR]

The key function of lubricants is to reduce the friction, wear, and heat between the parts that are in contact with each other. The main applications of the lubricants are to control temperature, and reduction in wear and corrosion of the machinery. Keeping in mind the importance of lubrication and its applications in varied machines. The goal of this research is to inspect the heat transmission impact in the magnetohydrodynamic flow of Jeffrey liquid near a stagnation point through a lubricated surface. Lubrication is accomplished by a shear-thinning liquid. The velocity, continuity, and shear stress, amalgamated with power-law fluids, are used to develop interfacial conditions. The exclusivity of the anticipated model is the inclusion of variable thermal conductivity and diffusion coefficients in the existence of homogeneous-heterogeneous reactions. Using the Keller–Box finite-difference approximation approach, the numerical results are accomplished. The outcomes are portrayed and tabulated in the form of diagrams and tables, respectively. It is witnessed that a greater magnetic field affects the fluid flow velocity and the drag force coefficient. Moreover, it is also inferred that the heat transfer rate dwindled for the greater thermal conductivity parameter. Authentication of the presented model is also part of this investigation. [ABSTRACT FROM AUTHOR]

The present study investigates the significance of activation energy during chemical reactions, thermal radiations and temperature gradient of 3-D steady Magnetohydrodynamic Casson nanofluid flow (MHDCNFM) in Darcy−Forchheimer medium over an oscillating disk by using an intelligent numerical-based computing solver through the Levenberg-Marquardt backpropagation neural network scheme (LMBNNS). The adjusted Buongiorno model is utilized to develop the system of partial differential equations (PDEs) for MHDCNFM, and further, by invoking Von Karman similarity transformation, the system of governing PDEs is turned out into ordinary differential equations (ODEs). First, a data set for the magnetohydrodynamic Casson nanofluid flow model (MHDNNFM) is generated for a range of sundry parameters for the radial velocity, tangential velocity, heat distribution and concentration profile by the variations of Casson parameter, magnetic parameter, Brownian motion parameter, thermophoresis parameter, Forchheimer parameter, activation energy parameter, chemical reaction parameter, stretching parameter, porosity parameter and Schmidt number through the Lobatto IIIA technique, and after this, by applying an intelligent computing algorithm through nftool training, testing and validation steps are taken into account to find out the approximate solution for various cases. The designed solver LMBNNS is used to solve the MHDCNFM through mean squared error (MSE), regression, gradient analysis and histogram studies. [ABSTRACT FROM AUTHOR]

Heat is absorbed from radiations of the sun by a solar collector, concentrated, and then transmitted to an active nanofluid. The flow of Casson nanofluid is utilized in Parabolic Trough Solar Collector (PTSC) in the present analysis over an infinite and porous sheet. Ordinary differential equations are derived in nonlinear form and solved using suitable similarity transformation reducing into boundary conditions. Keller box method was employed to solve the system of ODEs. Results for nanofluids of Copper-engine oil (Cu-EO), as well as Iron (II, III) oxide-engine oil (Fe3O4-EO), were examined and detailed. With the help of the induced magnetic factor, the rate of heat transfer decreased while the parameter of skin resistance increased prominently. While using Cu/Fe3O4-EO as base fluid, the rate of heat transfer is an important factor. Total enhancement in the thermal efficiency of Cu-EO on Fe3O4-EO has a minimum value of 2.7% while the maximum value is 18.5%. [ABSTRACT FROM AUTHOR]

The use of improved generalized Riccati equation mapping method has been demonstrated to find some new exact travelling wave solutions to space-time fractional non-liner double dispersive equation (DDE). The equation is used for modelling wave propagation in elastic inhomogeneous Murnaghan's rod. We have used Caputo's fractional derivative to achieve the fractional version of Murnaghan's rod equation. Improved generalized Riccati equation mapping method proves to be very effective tool to find a variety of soliton solutions. As a result, we found many new and general solutions including dark, combined dark-bright, singular periodic wave, combined singular periodic wave solutions and rational solutions. We have simulated the solitons, to check their types, with the help of graphs and all the solutions obtained in this article have been verified by back substitution in original equation by using Maple 17. [ABSTRACT FROM AUTHOR]

AbstractThe most common and contagious bacterial skin disease i.e. skin sores (impetigo) mostly affects newborns and young children. On the face, particularly around the mouth and nose area, as well as on the hands and feet, it typically manifests as reddish sores. In this study, a neuro-evolutionary global algorithm is introduced to solve the dynamics of nonlinear skin sores disease model (SSDM) with the help of an artificial neural network. The global genetic algorithm is integrated with local sequential quadratic programming (GA-LSQP) to obtain the optimal solution for the proposed model. The designed differential model of skin sores disease is comprised of susceptible (S), infected (I), and recovered (R) categories. An activation function based neural network modeling is exploited for skin sores system through mean square error to achieve best trained weights. The integrated approach is validated and verified through the comparison of results of reference Adam strategy with absolute error analysis. The absolute error results give accuracy of around 10−11 to 10−5, demonstrating the worthiness and efficacy of proposed algorithm. Additionally, statistical investigations in form of mean absolute deviation, root mean square error, and Theil’s inequality coefficient are exhibited to prove the consistency, stability, and convergence criteria of the integrated technique. The accuracy of the proposed solver has been examined from the smaller values of minimum, median, maximum, mean, semi-interquartile range, and standard deviation, which lie around 10−12 to 10−2. [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]

In this article, the Levenberg-Marquardt back propagation technique under the framework of neural networks (LMBT-NN) is incorporated. The heat and mass transfer characteristics of nanofluid (HMT-CNF) in a magneto-hydrodynamic (MHD) boundary layer over a vertical cone under convective boundary conditions have been investigated. The similarity transformation has been employed with the goal of transforming nonlinear partial differential equations (PDEs) into the system of ordinary differential equations (ODEs). A set of suggested data (LMBT-NN) is produced for some scenarios by modifying the radiation parameter (R), magnetic field parameter (M), buoyancy ratio parameter (Nr), chemical reaction parameter (Cr), thermophoresis factor (Nt), Lewis number (Le), and Brownian motion factor (Nb) within the applicability of the state-of-the-art Adams numerical technique. Using the (LMBT-NN) training, testing, and validation technique, the approximate solution of distinct instances has been validated, and for excellence, the proposed model has equated. To justify the proposed methodology (LMBT-NN), different error plots and numerical illustrations based on mean square errors, histogram plots, and regression analysis representations are prepared. With a correctness level ranging from E-9 to E-10, the recommended method has been observed based on the closeness of the suggested and reference outcomes. [ABSTRACT FROM AUTHOR]