Search

In this work, we propose a finite difference scheme for Caputo’s fractional derivative transport equation in time and space, with a zero-order term. A new error estimation of the approximate solution has been demonstrated. By introducing an approximation of the Caputo derivative, we proved that the convergence is of order 2-α in time, and 2-β in space, for 0

Significance: The CuO, Al2O3, and TiO2 nanoparticles find extensive applications in advanced chemical reaction-based thermal transport and quadratic convective nanofluids due to their exceptional thermal properties and chemical stability. Increased thermal conductivity of these nanoparticles used to enhance heat transfer in various chemical reactors, resistance to chemical degradation and photocatalytic reactors and solar energy applications. Motive: This study brings the investigation about quadratic convection-based thermal transport to infinite shear rate for magnetized ternary radiative cross nanofluid with homogeneous-heterogeneous chemical reactions. Water is taken as base fluid and three nanoparticles are Copper oxide (CuO), aluminium oxide (Al2O3), and titanium dioxide (TiO2). Heat transport analysis is made through quadratic convection, magnetic field and thermal radiation. Concentration of nanofluid is scrutinized though homogeneous-heterogeneous chemical reactions. Method: ology: Physical problem with assumptions generates the system of partial differential equations (PDEs) and these PDEs are transformed into ordinary differential equations (ODEs) through similarity variables. Furthermore, a unique combination of Bvp4c and Levenberg Marquardt neural network (LM-NN) schemes is utilized to fetch the numerical solutions. Bvp4c is utilized to solve the governing equations, while LM-NN serves to enhance predictive capabilities and capture intricate nonlinear relationships. Findings: Magnetic environment, chemical process, radiations effects and volumetric fraction of nanoparticles make better heat transfer efficiency and control.

Ternary hybrid nanofluids possess several potential applications in the modern science beyond just the heat transfer efficiency. A continuous research and advancements on binary and ternary hybrid nanofluids might lead towards new developments in many technological and scientific zones. Ongoing research interprets and distinguishes the novel attributes of the sodium alginate (Na.C6H7O6) based unary, binary and ternary nanofluids through a porous medium under induced magnetic field environment. The nano-composition of single-wall carbon nanotubes (SWCNT) with silver (Ag) and molybdenum dioxide (MoS2) gives rise to the binary (SWCNT-Ag/Na.C6H7O6) and ternary hybrid (SWCNT-Ag-MoS2/Na.C6H7O6) nanofluids respectively. A complex and highly nonlinear system of differential equations, obtained via the boundary layer approximations, is tackled numerically. An algorithmic approach, using MATLAB software, is incorporated to determine the iterative solutions. The efficiency as well as validity of the developed algorithm is confirmed by equating the results with the previous ones. The results evidently portray the fact that the magnetic Prandtl number and magnetic interaction parameter not only dissuade the induced magnetic field but also resist the fluids’ speed. With the larger values of activation energy parameter, higher will be the concentration of fluid.

In the current article, we establish the existence and uniqueness of solutions to the initial value problem for nonlinear implicit fractional differential equations with non-instantaneous impulses, including the Caputo-Fabrizio fractional derivative. This derivative encapsulates non-local and memory-dependent effects in the system's behavior. The problem's complexity arises from its implicit nature, where the relationships between variables are not directly specified. This inherent intricacy is further compounded by the introduction of non-instantaneous impulses, signifying abrupt, intermittent changes within the system at specific junctures, which in turn trigger sudden transitions. At its core, the initial value problem is concerned with deciphering a system's behavior based on its initial conditions, necessitating a solution that adheres to the given equation while considering the presence of non-instantaneous impulses. To derive the existence results, the study leverages established mathematical tools, specifically, the standard Banach's fixed point theorem and Darbo's fixed point theorem connected to Kuratowski's measure of noncompactness (KMN). Furthermore, the Hyers-Ulam stability (HU-stability) of the given problem is discussed, which, in turn, enhances the utility and reliability of these solutions in practical applications. In order to demonstrate the applicability of the discovered results for various values of δ, we construct some examples towards the end. The practical implications of these results extend to a wide range of fields, offering improved modeling, control, and understanding of complex systems.

The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models in two and three dimensions. We combined the Liouville–Caputo fractional derivative scheme with the Strang splitting algorithm for the temporal component and employed a meshless technique for spatial derivatives utilizing Lucas and Fibonacci polynomials. The rising demand for meshless methods stems from their inherent mesh-free nature and suitability for higher dimensions. Moreover, this approach demonstrates the effective approximation of solutions across both regular and irregular domains. Error norms were used to assess the accuracy of the methodology across both regular and irregular domains. A comparative analysis was conducted between the exact solution and alternative numerical methods found in the contemporary literature. The findings demonstrate that our proposed approach exhibited better performance while demanding fewer computational resources.

The phenomenon known as the Jeffrey-Hemal flow has become significantly important in diverse engineering and biological fields due to its use in the transportation of nanofluids across converging and diverging channels. The authors' current efforts are driven by the interdisciplinary development and study in this field. This research aims to examine the behavior of magnetized nanofluids as they flow through converging and diverging channels, taking into account the impact of a thermally balanced Darcy-Forchheimer permeable medium. The nanofluids are composed of copper oxide (CuO) and water. The second law of thermodynamics is used to formulate the concept of entropy generation. Channels are susceptible to the effects of Joule heating and solar radiation. The fundamental equations are converted from partial differential equations (PDEs) to ordinary differential equations (ODEs) by using suitable variables. The bvp4c scheming, an integrated MATLAB command, has been used for computational modeling. Graphical representations depict the impact of physical factors on velocity, entropy, and temperature. Furthermore, the influence of several factors on the Nusselt number is shown and analyzed. The findings demonstrate a positive correlation between temperature and greater Darcy and inertia values in converging/diverging channels, whereas the reverse trend is found in the case of divergent channels.

In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. On suggested problems, the third-order Caputo–Fabrizio derivative is the fractional operator applied. In this regard, the corresponding hybrid fractional integral equation is obtained by the Caputo–Fabrizio operator’s properties with the Green function’s aid. Then, we apply Dhage’s nonlinear alternative to the Schaefer type to prove the existence results. Finally, two examples are provided to confirm the validity of our main results.

In this work, we consider a coupled nonlinear viscoelastic Kirchhoff equations with degenerate damping, dispersion and source terms. Under suitable hypothesis, we will prove that when the initial data are large enough (in the energy point of view), the energy grows exponentially and thus so the L2(p+2)-norm.

In this paper, we investigate new types of nonlocal implicit problems involving piecewise Caputo fractional operators. The existence and uniqueness results are proved by using some fixed point theorems. Furthermore, we present analogous results involving piecewise Caputo-Fabrizio and Atangana–Baleanu fractional operators. The ensuring of the existence of solutions is shown by Ulam-Hyer’s stability. At last, two examples are given to show and approve our outcomes.

Abstract In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and general source terms. According to some suitable hypothesis, we study the blow-up of solutions. This is the general case of the recent results of Boulaaras’ works (Bull. Malays. Math. Sci. Soc. 43:725–755, 2020) and (Appl. Anal. 99:1724–1748, 2020).

Abstract In this article, we aim to investigate various formulae for the ( p , k ) $(p,k)$ -analogues of Gauss hypergeometric functions, including the integral transforms and the operators of fractional calculus. All the outcomes presented here are of general attractiveness and can yield a number of previous works as special cases.

Seagull Optimization Algorithm (SOA) is a metaheuristic algorithm that mimics the migrating and hunting behaviour of seagulls. SOA is able to solve continuous real-life problems, but not to discrete problems. The eight different binary versions of SOA are proposed in this paper. The proposed algorithm uses four transfer functions, S-shaped and V-shaped, which are used to map the continuous search space into discrete search space. Twenty-five benchmark functions are used to validate the performance of the proposed algorithm. The statistical significance of the proposed algorithm is also analysed. Experimental results divulge that the proposed algorithm outperforms the competitive algorithms. The proposed algorithm is also applied on data mining. The results demonstrate the superiority of binary seagull optimization algorithm in data mining application.

This paper presents ear recognition models constructed with Deep Residual Networks (ResNet) of various depths. Due to relatively limited amounts of ear images we propose three different transfer learning strategies to address the ear recognition problem. This is done either through utilizing the ResNet architectures as feature extractors or through employing end-to-end system designs. First, we use pretrained models trained on specific visual recognition tasks, inititalize the network weights and train the fully-connected layer on the ear recognition task. Second, we fine-tune entire pretrained models on the training part of each ear dataset. Third, we utilize the output of the penultimate layer of the fine-tuned ResNet models as feature extractors to feed SVM classifiers. Finally, we build ensembles of networks with various depths to enhance the overall system performance. Extensive experiments are conducted to evaluate the obtained models using ear images acquired under constrained and unconstrained imaging conditions from the AMI, AMIC, WPUT and AWE ear databases. The best performance is obtained by averaging ensembles of fine-tuned networks achieving recognition accuracy of 99.64%, 98.57%, 81.89%, and 67.25% on the AMI, AMIC, WPUT, and AWE databases, respectively. In order to facilitate the interpretation of the obtained results and explain the performance differences on each ear dataset we apply the powerful Guided Grad-CAM technique, which provides visual explanations to unravel the black-box nature of deep models. The provided visualizations highlight the most relevant and discriminative ear regions exploited by the models to differentiate between individuals. Based on our analysis of the localization maps and visualizations we argue that our models make correct prediction when considering the geometrical structure of the ear shape as a discriminative region even with a mild degree of head rotations and the presence of hair occlusion and accessories. However, severe head movements and low contrast images have a negative impact of the recognition performance.

Different strategies have been utilized by investigators with the intention of upgrading the thermal characteristics of ordinary liquids like water and kerosene oil. The focus is currently on hybrid nanomaterials since they are more efficient than nanofluids, so as to increase the thermal conductivity of fluids and mixtures. In a similar manner, this investigation is performed with the aim of breaking down the consistent mixed convection flow close to a two-dimensional unstable flow between two squeezing plates with homogeneous and heterogeneous reaction in the presence of hybrid nanoparticles of the porous medium. A sustainable suspension in the ethylene glycol with water is set by dissolving inorganic substances, iron oxide Fe3O4 and cobalt (Co), to form Fe3O4−Co/C2H6O2−H2O hybrid nanofluid. The numerical and analytical model portraying the fluid flow has been planned, and similitude conditions have been determined with the assistance of the same transformations. The shooting technique has been used to solve nonlinear numerical solution. To check the validity of the results obtained from the shooting mode, the Matlab built-in function BVP4c and Mathematica built-in function homotopy analysis method (HAM) are used. The influence of rising parameters on velocity, temperature, skin friction factor, Nusselt number, and Sherwood number is evaluated with the help of graphs and tables. It has been found in this work that to acquire a productive thermal framework, the hybrid nanoparticles should be considered instead of a single sort of nanoparticles. In addition, the velocities of both the hybrid nanofluids and simple nanofluids are upgraded by the mixed convection boundary, whereas they are decreased by the porosity. An augmentation in volumetric fraction of nanoparticles correlates to an increment in the heat transmission rate. It is also found that heat transfer rate for Fe3O4−Co/C2H6O2−H2O hybrid nanofluids (HNF) is better than that of the Fe3O4−C2H6O2−H2O of single nanofluids (SNF). This research shows that hybrid nanofluids play a significant part in the transfer of heat and in the distribution of nanofluids at higher temperatures.

Unsteady electrohydrodynamic hybrid nanofluid Al2O3‐Cu/H2O past a convective heat stretched/shrinked sheet is examined. A stagnation point fluid flow with velocity slip constrains and heat source or sink is deliberated. The combined set of PDEs is translated into ODEs by including approved similarity transformations. HAM is applied for the solution to the obtained nonlinear system. The magnetic input factor, Prandtl number, electric field factor, Eckert number, heat source factor, and unstable factor are the governing parameters. The impact of these factors on the temperature and velocity profiles features of the problem is considered with explanation. Intensification in values of electric and magnetic fields parameters enhanced the heat transfer rate. The greater Prandtl number lessens the temperature. Amplification in temperature is perceived for Eckert parameter. The heat transferred rate of hybrid nanofluid in the entire domain increases as the heat source increases, while the heat sink has the opposite effect. Skin friction and Nusselt number is increased for increasing values of magnetic field parameters. It is also noted that Nusselt number lessens for raising in Pr,E,and Ec. Furthermore, it is eminent that the hybrid nanofluid possesses better result compared to the nanofluid.

In this study, we consider the Fisher equation in bounded domains. By Faedo–Galerkin’s method and with a homogeneous Dirichlet conditions, the existence of a global solution is proved.

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and source terms without the Kirchhoff term. Under suitable hypothesis, we study the blow-up of solutions.

In this work, we study the bifurcation of limit cycles from the period annulus surrounding the origin of a class of cubic polynomial differential systems; when they are perturbed inside the class of all polynomial differential systems of degree six, we obtain at most fifteenth limit cycles by using the averaging theory of first order.

We study the limit cycles of the fifth-order differential equation x⋅⋅⋅⋅⋅−ex⃜−dx⃛−cx¨−bx˙−ax=εFx,x˙,x¨,x⋯,x⃜ with a=λμδ,b=−λμ+λδ+μδ,c=λ+μ+δ+λμδ,d=−1+λμ+λδ+μδ,e=λ+μ+δ, where ε is a small enough real parameter, λ,μ, and δ are real parameters, and F∈C2 is a nonlinear function. Using the averaging theory of first order, we provide sufficient conditions for the existence of limit cycles of this equation.

In this article, we discuss certain properties for generalized gamma and Euler’s beta matrix functions and the generalized hypergeometric matrix functions. The current results for these functions include integral representations, transformation formula, recurrence relations, and integral transforms.

Accurate and early detection of machine faults is an important step in the preventive maintenance of industrial enterprises. It is essential to avoid unexpected downtime as well as to ensure the reliability of equipment and safety of humans. In the case of rotating machines, significant information about machine’s health and condition is present in the spectrum of its vibration signal. This work proposes a fault detection system of rotating machines using vibration signal analysis. First, a dataset of 3-dimensional vibration signals is acquired from large induction motors representing healthy and faulty states. The signal conditioning is performed using empirical mode decomposition technique. Next, multi-domain feature extraction is done to obtain various combinations of most discriminant temporal and spectral features from the denoised signals. Finally, the classification step is performed with various kernel settings of multiple classifiers including support vector machines, K-nearest neighbors, decision tree and linear discriminant analysis. The classification results demonstrate that a hybrid combination of time and spectral features, classified using support vector machines with Gaussian kernel achieves the best performance with 98.2% accuracy, 96.6% sensitivity, 100% specificity and 1.8% error rate.