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In this study, the Laguerre wavelet-oriented numerical scheme for nonlinear first and second-order delay differential equations (DDEs) is offered. The proposed technique is dependent on the truncated series of the Laguerre wavelets approximation of an unknown function. Here, we transform the different ordered DDEs into a system of non-linear algebraic equations with the help of limit points of a sequence of collocation points. Four nonlinear illustrations are involved to prove the efficiency of the planned technique. Obtained results are equated with the current results, indicating the proposed technique’s accuracy and efficiency.

In this research work, we employ the unified method, the extended sinh-Gordon equation expansion method (ShGEEM), and the extended rational sine-cosine/sinh-cosh method to derive the novel optical solitons solutions of the (2+1)-dimensional nonlinear dynamical conformable fractional generalized Schrödinger system in monomode optical fibers. We extract the optical soliton solutions in diverse forms like, dark, bright, combinations of dark-bright, periodic, and singular solutions, that are presented by trigonometric functions, and hyperbolic functions. The employed procedures are useful for clarifying nonlinear partial differential equations (NLPDEs) and secure new exact solutions in addition to previously recovered ones. The accuracy of these answers has been verified for all extracted results using the Mathematica. The 3D surface plots, 2D line plots, and associated contour graphs are used to analyze the obtained solutions to visualize and support the theoretical conclusions using appropriate parameter values. The findings of this research demonstrate the efficacy of the approaches taken in enhancing nonlinear dynamical behavior.

The goal of this study is to develop churn models for sellers on the e-commerce marketplace by using machine learning methods. In this sense, three approaches were applied for developing the models. The dataset used in this study includes ten features, which are maturity type, maturity interval, city of the seller, total revenue of the seller, total transaction of the seller, sector type of the seller, business type of the seller, sales channel, installment option and discount type. Random Forest (RF) and Logistic Regression (LR) were used for churn analysis in all of the approaches. In the first approach, models were developed without applying preprocessing operations on the dataset. In the second and third approaches, under sampling and oversampling methods, respectively, were used to balance the data set. By using stratified cross validation on the dataset, F-Scores of the churn models were obtained. The results show that F-Scores were 0.76, 0.71 and 0.92 for the three approaches developed with RF, and 0.84, 0.68 and 0.69 for the three approaches developed with LR, respectively.

In this study, some new inequalities for n-times differentiable strongly s-convex functions are introduced. These inequalities are obtained via the perturbed trapezoid inequality. We obtain a better bound for the mentioned inequalities with the strongly s-convex functions. nth derivatives of absolute values of the handled functions are strongly s-convex. Finally, the theorems presented for strongly s-convex functions are reduced to the ones given for s-convex functions when the constant from strongly s-convexity vanishes.

In this article, we develop the natural transform in terms of the M-derivative. We improve the basic notions for this new interesting version of the fractional transform. We introduce the properties and relations of certain functions for the natural transform of the M-derivative. The natural transform with the M-derivative is the more general version of the natural transform for the conformable operator. Furthermore, this method is successfully applied to find the general solutions of some fractional differential equations with M-derivative. We propose a significant spectral data with boundary conditions under M-Sturm-Liouville problem. We offer the representation of the solution for the M-Sturm-Liouville problem, depending on both the boundary and initial conditions. Our main aim is to extract the representation of solution of the M-Sturm-Liouville problem by using the natural transform and to observe the problem by supporting the spectral structure of the M-Sturm Liouville problem with graphs. Finally, these results show that our new approach is simple, effective and accurate.

In this short paper, we give the proof of the Ambarzumyan theorem by zeros of eigenfunctions (nodal points) different from eigenvalues for the one-dimensional p-Laplacian eigenvalue problem. We show that the potential function q(x) is zero if the spectrum is in the specific form. We consider this theorem for p-Laplacian equation with periodic and anti-periodic cases. If p = 0, results are coincided with the results given for Sturm-Liouvile problem.

The aim of this work is to solve a mathematical model based on the migration and emigration effects. The designed mathematical model shows one of the forms of prey-predator. The migration factor represents a step function for both normal and individuals that is restrictions or movement of the people. The numerical solutions of the designed model are presented using the stochastic computational schemes based on the artificial neural networks (ANNs) together with the Levenberg-Marquardt back propagation (LMB), i.e., ANNs-LMB for solving the model based on the migration and emigration effects. Three different cases have been performed to solve the model based on the migration and emigration effects with the ANNs-LMB solver in terms of authentication, training, sample statistics and testing. The selection of the data is chosen as 80%, 10%, 10% for training, testing and authentication, respectively. The numerical obtained results through the ANNs-LMB of the model based on the migration and emigration effects will be compared with the Runge-Kutta method. The results of the model based on the migration and emigration effects using the ANNs-LMB are provided to reduce the mean square error (MSE). For the capability and efficiency of the proposed ANNs-LMB, the numerical results are provided using the correlation, error histograms, regression and MSE.

This article applies the sextic B-spline collocation scheme to obtain the approximate solution of the Generalized Equal Width (GEW) wave equation. The accuracy of the proposed technique is discussed over three test applications including the single soliton wave, interaction of soliton waves and Maxwellian initial problem while we are getting the three invariant A₁, A₂, A₃ and two error norms referred as to L₂ and L_∞. Applying the Von Neumann algorithm, the linearized technique is unconditionally stable. Our computational data show the superiority of results over those existing results in the literature review.

In this work, we investigate the dynamical study of the (1+1)-dimensional Mikhailov-Novikov-Wang (MNW) equation via the unified method. This technique is used to obtain the soliton solutions, including the trigonometric function solution, the periodic function solution, the exponential function solution, the elliptic function solution, and other soliton-form solutions. All the obtained results in this work utilizing an effective unified method contributes to gain a better understanding of the physical meaning and behavior of the equation, which sheds light on the significance of investigating diverse nonlinear wave phenomena in physics and ocean engineering. These derived results are entirely new and never repeated in the previous works done by the other authors. For the interest of visual presentation and physical illustrations, we plot the graphical demonstrations of some of the specified solutions in 3-dimensional, contour, and 2-dimensional plots by using Mathematica software. Consequently, we observe that the acquired solutions of the MNW equations are anti-bell-shape, kink wave solution, solitary wave, periodic solution, multisoliton, and different types of soliton solutions.

This paper focuses on the classification of forest biomass into two categories: premature and mature forest biomass. The third variable considered is industrialization. The growth of the wood-based industry is believed to be closely tied to the population of mature forest biomass. Any scarcity of the mature population could have a negative impact on industrialization. So, pre-mature forest biomass is provided as an alternative for industrial growth. The industrialization growth is assumed to be based on a modified Leslie-Gower equation. The positivity and boundedness of the system are calculated using the comparison theorem. Stability analysis is done about nonzero equilibrium points with the help of the Routh-Hurwitz theorem. When there is no delay in the system, the system is stable. At τ< 1.8, the system shows asymptotic stability, but at τ ≥ 1.8, system shows Hopf-bifurcation and periods oscillations occur. Further, sensitivity analysis is examined about different parameters of the systems. MATLAB is used to draw the numerical simulation.