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In this article, we first consider approach of optical spherical magnetic antiferromagnetic model for spherical magnetic flows of ϒ\Upsilon -magnetic particle with spherical de-Sitter frame in the de-Sitter space S12{{\mathbb{S}}}_{1}^{2}. Hence, we establish new relationship between magnetic total phases and spherical timelike flows in de-Sitter space S12{{\mathbb{S}}}_{1}^{2}. In other words, the applied geometric characterization for the optical magnetic spherical antiferromagnetic spin is performed. Moreover, this approach is very useful to analyze some geometrical and physical classifications belonging to ϒ\Upsilon -particle. Besides, solutions of fractional optical systems are recognized for submitted geometrical designs. Geometrical presentations for fractional solutions are obtained to interpret the model. These obtained results represent that operation is a compatible and significant application to restore optical solutions of some fractional systems. Components of models are described by physical assertions with solutions. Additionally, we get solutions of optical fractional flow equations with designs of our results in de-Sitter space S12{{\mathbb{S}}}_{1}^{2}.

This study aims to analyze the mass transfer and entropy generation in the flow system of chemically reactive, thermal radiative hybrid nanofluids (Al2O3/Cu with H2O as base fluid) flow across flat stretching porous surfaces in the presence of viscous dissipation and transverse magnetic field. The governing partial differential equations are converted into a set of ordinary differential equations by applying a group of self-similarity transformations. The resulting differential equations are solved using the Bvp4c technique in MATLAB. The impact of several physical parameters has been examined the velocity, heat, and mass transfer components of the fluid. To optimize the complete heat transfer process, the consequences of all physical parameters are discussed on entropy generation and Bejan number and presented graphically. It is observed that velocity increases with the increase in magnetic parameter M because pressure force dominates over Lorentz force, temperature increases with the rise of Ec, concertation reduces with the enhancement of chemical reaction parameter delta, and the Bejan number decreases with the increase in Br; however, reverse phenomena are observed with increasing the value of the magnetic number and entropy increases with the rise of magnetic parameter M. Due to the increase in magnetic parameter M, drag force is accelerated, which leads to increase in entropy, With an increment in Pr and Ec, the heat exchange rate declines although the skin friction coefficient and mass transfer remain constant. There are several significant applications of the study of thermal analysis of hybrid nanofluid flows in numerous mechanical processes, such as extrusion or metal manufacturing processes, heat transportation in biological tissues, cooling of electric devices, high-size refrigeration, hydroelectric dams, and fuel systems. [ABSTRACT FROM AUTHOR]

Numerical unsteady approach based on Galerkin method with the inclusion of adaptive mesh was executed in this paper to simulate the freezing of water within a container. The domain has two triangular and trapezoidal cold surfaces and two adiabatic walls. The governing equations show the domination of conduction and transient source term has been involved. Galerkin method for modeling was applied and good accommodation has been reported based on comparison with previous data. Adding nano-powders makes the amount of heat to be released with stronger conduction and freezing time decreases about 26.76% when m = 8. 6. Augmenting the fraction of powders can make the rate of process increase. For the greatest fraction of powders, an augmenting shape factor can enhance the speed of process about 6.95%. [ABSTRACT FROM AUTHOR]

This article studies dark, bright, trigonometric and rational optical soliton solutions to the perturbed nonlinear Schrödinger–Hirota equation (PNLSHE). Hence, we have examined two cases: first, restrictions have been done to the third-order (TOD) (γ) as constraint relation, and the coupling coefficients (σ) is obtained as well as the velocity of the soliton by adopting the traveling wave hypothesis. Second, the TOD and the coupling coefficients are non-zero value, sending back to the PNLSHE, which has been studied in refs. [4,10,16] recently. By employing two relevant integration technics such as the auxiliary equation and the modified auxiliary equation method, miscellaneous optical solitary wave is obtianed, which is in agreement with the outcomes collected by the previous studies [4,16]. These results help in obtaining nonlinear optical fibers in the future.

This paper presents a novel hybrid approach, fusing genetic algorithms (GA) and penguin search optimization (PSeOA), to address the flow shop scheduling problem (FSSP). GA utilizes selection, crossover, and mutation inspired by natural selection, while PSeOA emulates penguin foraging behavior for efficient exploration. The approach integrates GA's genetic diversity and solution space exploration with PSeOA's rapid convergence, further improved with FSSP-specific modifications. Extensive experiments validate its efficacy, outperforming pure GA, PSeOA, and other metaheuristics. [ABSTRACT FROM AUTHOR]

In this paper, the Poiseuille flow of non-isothermal couple stress fluid of Reynolds model between two heated parallel inclined plates has been studied. The strongly nonlinear coupled ordinary differential equations have been investigated using the Asymptotic Homotopy Perturbation method (AHPM) and the Optimal Homotopy Asymptotic Method with DJ Polynomials (OHAM-DJ). Employing both these techniques, the approximate solutions for velocity profile, temperature distributions, shear stress, average velocity and volumetric flow rate have been achieved. The results obtained using both these methods are in the form of infinite series, hence the results can be obtained easily. Comparison of various results, obtained through these methods, is carried out. Here, it is worth to mention that the results gained by both these approaches are in excellent resemblance. The effect of different parameters on the flow problem has been studied numerically as well as presented graphically. [ABSTRACT FROM AUTHOR]

This research paper investigates the numerical solutions of the predator–prey model through five recent numerical schemes (Adomian decomposition, El Kalla, cubic B‐spline, extended cubic B‐spline, exponential cubic B‐spline). We investigate the obtained computational solutions via the modified Khater methods. This model is considered as a well‐known bimathematical model to describe the prototype of an excitable system. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. The accuracy of the obtained numerical solutions is investigated by calculating the absolute error between the exact and numerical solutions. Many sketches are given to illustrate the matching between the exact and numerical solutions. [ABSTRACT FROM AUTHOR]

A survey of results on Grüss-type inequalities associated with a variety of fractional integral and differential operators is presented. The fractional differential operators includes, Riemann-Liouville fractional integral operators, Riemann-Liouville fractional integrals of a function with respect to another function, Katugampola fractional integral operators, Hadamard's fractional integral operators, k-fractional integral operators, Raina's fractional integral operators, tempered fractional integral operators, conformable fractional integrals operators, proportional fractional integrals operators, generalized Riemann-Liouville fractional integral operators, Caputo-Fabrizio fractional integrals operators, Saigo fractional integral operators, quantum integral operators, and Hilfer fractional differential operators. [ABSTRACT FROM AUTHOR]