In the present analysis, an unsteady MHD mixed convection flow is scrutinized for a non-Newtonian Casson hybrid nanofluid in the stagnation zone of a rotating sphere, resulting from the impulsive motion of the angular velocity of the sphere and the velocity of the free stream. A set of linearized equations is derived from the governing ones, and these differential equations are solved numerically using the hybrid linearization–differential quadrature method. The surface shear stresses in the $x$- and $y$-directions and the surface heat transfer rate are improved due to the Casson ${\beta }_o$, mixed convection $\alpha$, rotation $\gamma$ and magnetic field $M$ parameters. In addition, as nanoparticles, the solid volume fraction (parameter $\varphi$) increases, and the surface shear stresses and the rate of heat transfer are raised. A comparison between earlier published data and the present numerical computations is presented for the limiting cases, which are noted to be in very good agreement.

An excellent e-commerce logistic cycle is based on reducing the delivery time to satisfy customers, accelerating the distribution chain activities at each delivery station, increasing the transported stowage objects for mobilization parallelograms containers to ingest most orders, and reducing the unused area. Because the stowage steps are considered an NP-complexity, the authors introduce the Oriented Stowage Map (OSM) using one of the heuristic methods (i.e., the camel algorithm) that are programmed by the C-sharp software to be easily managed via the Internet of Things (IoT), which is embedded in the distribution chain. The authors called it Oriented Stowage’s Map by Camel algorithm “OSM-CA”. This methodology is considered one of the mat-heuristic approaches (i.e., decomposition metaheuristics) because we resorted to using mathematical steps (branch-and-bound). The OSM-CA reduces transport costs by 7% and delivery time by 14%. Additionally, it shows superiority over the solo Ant-colony for stowage less than 50 boxes by 10% and over the solo camel algorithm by 27%, while for more than 50 boxes, the OSM-CA superiority by 30% over the ant colony, and 17% over the camel algorithm. Creating the map in the proposed way takes 70% less time than using mathematical models, especially for a large number of orders, more than 200.

This paper solves a generalized class of first-order fractional ordinary differential equations (1st-order FODEs) by means of Riemann–Liouville fractional derivative (RLFD). The principal incentive of this paper is to generalize some existing results in the literature. An effective approach is applied to solve non-homogeneous fractional differential systems containing $2n$ periodic terms. The exact solutions are determined explicitly in a straightforward manner. The solutions are expressed in terms of entire functions with fractional order arguments. Features of the current solutions are discussed and analyzed. In addition, the existing solutions in the literature are recovered as special cases of our results.

Scholars seek to recycle wasted energy to produce electricity by integrating thermoelectric generators (TEGs) with internal combustion engines (ICE), which rely on the electrical conductivity, β, of the thermal conductor strips. The TEG legs are alloyed from iron, aluminum and copper in a strip shape with specific characteristics that guarantee maximum thermo-electric transformation, which has fluctuated between a uniform, Gaussian, and exponential distribution according to the structure of the alloy. The ICE exhaust and intake gates were chosen as the TEG sides. The digital simulator twin model checks the integration efficiency through two sequential stages, beginning with recording the causes of thermal conductivity failure via filming and extracting their data by neural network procedures in the feed of the second stage, which reveal that the cracks are a major obstacle in reducing the TEG-generated power. Therefore, the interest of the second stage is predicting the cracks’ positions, P_i,j, and their intensity, Q_P, based on the ant colony algorithm which recruits imaging data (STTF-NN-ACO) to install the thermal conductors far away from the cracks’ positions. The proposed metaheuristic (STTF-NN-ACO) verification shows superiority in the prediction over [Mat-ACO] by 8.2% and boosts the TEGs’ efficiency by 32.21%. Moreover, increasing the total generated power by 12.15% and working hours of TEG by 20.39%, reflects reduced fuel consumption by up to 19.63%.

Recycling plastic waste (RPW) benefits the ecological footprint. Therefore, the authors test its mixing by magnetic hydrodynamic MHD nanofluid materials such as alumina in two sizes (${\beta }_{core}, {\beta }_{skin}$) prepared into a new device called the incubator installed in the desktop injection machine to enhance its solubility by taking advantage of the mixture’s heat via defining the oblique stagnation-point slip flow (OSPSF) of a nanofluid in two dimensions. The paper has been innovative in mathematically identifying the operating parameters’ values for the injection flow mechanism (IFM) via controlling in Riga magnetic field and piston orifice pressure using a meta-heuristic algorithm called WSA. The proposed (IFM) is used to experimentally enhance the mixture properties via parameters’ control to meet the output quality and predict the control equation for the Riga plate. IFM controls the amount of pushed nanoparticles in the mixture with a ratio of plastic to aluminum approximate by 96.1%: 3.9%. The defects were reduced by approximately 23.21%, with an increasing system performance of 70.98%.

In this study, a novel method called the q-homotopy analysis transform method (q-HATM) is proposed for solving fractional-order Kolmogorov and Rosenau–Hyman models numerically. The proposed method is shown to have fast convergence and is demonstrated using test examples. The validity of the proposed method is confirmed through graphical representation of the obtained results, which also highlights the ability of the method to modify the solution’s convergence zone. The q-HATM is an efficient scheme for solving nonlinear physical models with a series solution in a considerable admissible domain. The results indicate that the proposed approach is simple, effective, and applicable to a wide range of physical models.