Moataz Alosaimi

Symmetric quantum calculus offers a dynamic framework for investigating the various classes of functions. However, the symmetric quantum operators become inconclusive at certain points. To overcome the limitations of existing calculi, operators over finite intervals have been extensively explored. To develop a more general and applicable setup, we introduce the symmetric quantum derivative and integral operators governed by an arbitrary point. Furthermore, we discuss structural properties of the newly developed operators and special cases to relate to the existing literature. Then, by applying the concepts of general symmetric quantum operators, convexity, Lipschitzian property, and Korkine’s identity, we derive a new set of inequalities, including Hermite–Hadamard, Ostrowski, Hólder, Minkowski, and Gruss-type inequalities, respectively. The proposed inequalities are useful to derive the bounds of generalized symmetric quantum integrals. Furthermore, the newly developed operators can be applied to study the impulsive difference equations and their dynamics. Additionally, a feed-forward ANN model is established to approximate the analytic expressions involved in inequalities and to observe the consistency of integral bounds. The results of the ANN analysis suggest a significant agreement between analytical solutions and approximations. Lastly, we focus on an applicable analysis of our derived results. The generic nature of operators will lead to new developments in quantum calculus. The hybrid approach evolved in this study will bring new applicable insights to the mathematical analysis.

This study explores the influence of viscous dissipation and variable density on heating efficiency and mass flux in magneto-hydrodynamic Oldroyd-B fluid flow over a polymer stretching surface with Soret and Dufour effects. The heat convective boundary conditions are used for the increment of thermal sequence. To incorporate nonlinear partial differential equations into a standard differential scheme, the appropriate transformation is used. The flow equations are reduced to nonlinear differential expressions and then numerically solved using the effective Keller box approach. The Newton–Raphson approach is applied to calculate the unknown quantities over the polymer sheet. The evaluation of the controlling flow factors, such as Prandtl quantity Pr, Deborah numbers β1, β2, Biot number γ, mixed convection parameter λ, magnetic parameter M, Eckert parameter Ec, on thermal distribution, mass distribution, and velocity profiles is calculated significantly. It is observed that a significant increase in the fluid temperature is evaluated at a minimal Prandtl number Pr = 1.5 but a maximum value is observed at a larger magnetic factor M = 3.5. Skin friction and the rate of mass flux are increased at a higher choice of heat convection parameter.

Understanding the mechanics of n-immiscible coating layers on electrical wires can improve efficiency, design, and practical applications by optimizing their performance. This paper theoretically analyzes the flow and heat transfer of n-immiscible coating layers on a wire in an annulus die. A mathematical model of n-immiscible coating layers is developed. Formulated sets of linear ordinary differential equations are solved for closed-form solutions. The dynamic viscosity μk, Brinkman number Brk, and thermal conductivity ratio χ emerged as flow control parameters. The effects of the parameters involved in the velocity, temperature, coating thickness, and shear stress of five-immiscible coating layers are observed. It is delineated that internal resistance to flow increases with an increase in dynamic viscosity, thus affecting momentum transfer. This, in turn, reduces shear stress and alters temperature, velocity distribution, and coating thickness. The temperature rise is primarily due to viscous dissipation, while thermal diffusion works to lower it. Furthermore, improved thermal conductivity also contributes to a reduction in temperature. The analysis of five-immiscible coating layers provides insights and knowledge applicable to a coating system with a desired number of coating layers by utilizing the expressions derived for n-immiscible coating layers.

This work investigates the inverse boundary value problem for a sixth-order Boussinesq equa-tion, where the time-dependent coefficients are unknown. The primary objective is to determine these unknown coefficients and solve the corresponding problem. The original problem is transformed into an equivalent auxiliary problem. By utilizing the contraction mapping method, we prove the existence and uniqueness of the solution for the auxiliary problem. Consequently, we establish the existence and uniqueness of a classical solution to the initial problem.

This evaluation inspects an analytical computation of magneto carboxymethylcellulose (CMC)–water-based hybrid nanofluid containing molybdenum disulfide (MoS ₂ ) and zinc oxide (ZnO) nanoparticles through an immersed porous surface. The flow is considered an exponential surface along a hybrid nanofluid. The energy and mass expression has been computed through thermal radiation, heat generation/absorption. The plate temperature obtains higher to T w {T}_{w} , and the concentration of species C w {C}_{w} surrounding the plate climbs linearly over time. Employing nondimensional factors allows a model’s leading equation to transform into dimensionless. The Laplace transformation methods are employed to address the nondimensional differential equations of hybrid nanofluid in the MATHEMATICA 12.0 software. The impact of developing factors on temperature, concentration, velocity, drag force, Nusselt, and Sherwood number is explored which are examined graphically and tabular form for the MoS ₂ + ZnO/CMC–water and MoS ₂ /CMC–water. The flow variables such as porosity flow, radiative variable, heat source variable, Prandtl number, chemical reaction, and Schmidt number. It is concluded that the greater estimation of porosity and magnetic variable declined the velocity distribution for the MoS ₂ + ZnO/CMC–water and MoS ₂ /CMC–water. Thermal radiation causes the temperature to rise distribution but declining phenomena is observed for Prandtl number. The porosity of flow and magnetic field enhances the drag force by 32.13–55.76%.