rss_2.0International Journal of Mathematics and Computer in Engineering FeedSciendo RSS Feed for International Journal of Mathematics and Computer in Engineering Journal of Mathematics and Computer in Engineering Feed industrial growth through alternative forest biomass resources: A mathematical model using DDE<abstract><title style='display:none'>Abstract</title> <p>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&lt; 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.</p> </abstract>ARTICLEtrue nature of analytical soliton solutions of the (1+1)-dimensional Mikhailov-Novikov-Wang equation using the unified approach<abstract><title style='display:none'>Abstract</title> <p>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 <italic>Mathematica </italic>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.</p> </abstract>ARTICLEtrue the generalized equal width wave equation via sextic -spline collocation technique<abstract><title style='display:none'>Abstract</title> <p>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 <italic>A</italic><sub>1</sub>, <italic>A</italic><sub>2</sub>, <italic>A</italic><sub>3 </sub>and two error norms referred as to <italic>L</italic><sub>2 </sub>and <italic>L</italic><italic><sub>∞</sub></italic>. 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.</p> </abstract>ARTICLEtrue the stochastic observation for the nonlinear system of the emigration and migration effects via artificial neural networks<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue theorem by zeros of eigenfunction<abstract><title style='display:none'>Abstract</title> <p>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 <italic>p</italic>-Laplacian eigenvalue problem. We show that the potential function <italic>q</italic>(<italic>x</italic>) is zero if the spectrum is in the specific form. We consider this theorem for <italic>p</italic>-Laplacian equation with periodic and anti-periodic cases. If <italic>p </italic>= 0, results are coincided with the results given for Sturm-Liouvile problem.</p> </abstract>ARTICLEtrue of solution the M-Sturm-Liouville problem with natural transform<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue -times differentiable strongly -convex functions<abstract><title style='display:none'>Abstract</title> <p>In this study, some new inequalities for <italic>n</italic>-times differentiable strongly <italic>s</italic>-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 <italic>s</italic>-convex functions. <italic>nth </italic>derivatives of absolute values of the handled functions are strongly <italic>s</italic>-convex. Finally, the theorems presented for strongly <italic>s</italic>-convex functions are reduced to the ones given for <italic>s</italic>-convex functions when the constant from strongly <italic>s</italic>-convexity vanishes.</p> </abstract>ARTICLEtrue learning based churn analysis for sellers on the e-commerce marketplace<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue analysis of exact solitons solutions in monomode optical fibers to the generalized nonlinear Schrödinger system by the compatible techniques<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue approach for the solution of nonlinear variable delay differential equations<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue backpropagation neural network procedures for the consumption of hard water-based kidney function<abstract> <title style='display:none'>Abstract</title> <p>Water resources in Nusa Tenggara Timur have great concentrations based on magnesium and calcium ions thus being referred to as “hard water”. Prolonged hard water consumption has become a reason of kidney disfunction that can cause additional illnesses, like cerebrovascular pathologies and diabetes. Hence, it is crucial to comprehend how drinking hard water affects renal functions. The current study shows the kidney dysfunction model based on hard water consumption by applying the stochastic procedures of the Levenberg-Marquardt backpropagation neural networks (LMBNNs). The kidney dysfunction model of hard water consumption depends upon human components and water. Human dynamics is further divided into susceptible, infected and recovered, while water components are categorized into calcium and magnesium concentration. The log-sigmoid transfer function along with 20 hidden neurons is used to present the solutions of the model. Three cases of the model have been numerically stimulated and the correctness of the stochastic technique is perceived by using the comparison of proposed and reference Adam databased solutions along with the negligible absolute error. Training, validation and testing performances have been applied to reduce the values of the mean square error. Moreover, the statistical performances using the transition of state, error histograms and regression/correlation have been validated to authenticate the reliability of the scheme.</p> </abstract>ARTICLEtrue SIZR model of Zombie infection<abstract> <title style='display:none'>Abstract</title> <p>This research paper investigates the SIZR model related to Zombie infection outbreaks according to a time-dependent infection rate. The proposed model is extended to the fractional order using different fractional derivative operators. The solution of the proposed model by numerical schemes, is briefed. Graphical representations provide us with a better understanding of this mathematical model. Lastly, as observed in movies, we conclude that Zombie infections can generate the destruction and collapse of human development and it is of paramount importance to deal with Zombies as early as possible in order to avoid putting our civilization under threatening and destructive circumstances.</p> </abstract>ARTICLEtrue solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method<abstract> <title style='display:none'>Abstract</title> <p>The Pseudo-Hyperbolic Telegraph partial differential equation (PHTPDE) based on the Caputo fractional derivative is investigated in this paper. The modified double Laplace transform method (MDLTM) is constructed for the proposed model. The MDLTM was used to obtain the analytic solution for the pseudo-hyperbolic telegraph equation of fractional order defined by the Caputo derivative. The proposed method is a highly effective analytical method for the fractional-order pseudo-hyperbolic telegraph equation. A test problem was presented as an example. Based on the results, it is clear that this method is more convenient and produces an analytic solution in fewer steps than other methods that require more steps to have an identical analytical solution. This paper claims to provide an analytic solution to the fractional order pseudohyperbolic telegraph equation order using the MDLTM. An analytical solution leads to an exact, closed-form solution that can be expressed in mathematical functions or known operations. Obtaining analytic solutions to PDEs is often challenging, especially for fractional order equations, making this achievement noteworthy.</p> </abstract>ARTICLEtrue analysis of a Tumor Growth model under the effect of fractal fractional Caputo-Fabrizio derivative<abstract> <title style='display:none'>Abstract</title> <p>Fractal-fractional derivatives, which are still rather new, are frequently used to look into the complexities of an issue. Today, tumors are a prevalent and difficult-to-treat condition. The Caputo-Fabrizio-fractal-fractional derivative, which is a non-singular derivative,. has been used to explore the tumor-growth model quantitatively and numerically. By using fixed-point theorems, it has been demonstrated that the model underneath the Caputo-Fabrizio-fractal-fractional derivative exists and is unique. The Ulam-Hyres stability of the model was evaluated using non-linear analysis. Using Lagrangian-piecewise interpolation and the fundamentals of fractional calculus, we can develop an algorithm that will enable us to determine the numerical solutions for the new model. In order to show the method’s dependability and effectiveness, numerical simulations are also included. Utilizing an exponential-decay kernel, we evaluated the dynamics of the Tumor Growth model to see if the non-singular fractal fractional operator offered better dynamics for the model under consideration.</p> </abstract>ARTICLEtrue analytical solutions and modulation instability analysis for the nonlinear (1+1)-dimensional Phi-four model<abstract> <title style='display:none'>Abstract</title> <p>This paper deals with the nonlinear (1+1)-dimensional Phi-four equation in the sense of the Katugampola operator, which can be used to model a variety of real-world applications. To solve this equation, we propose a generalized double auxiliary equation method that yields several new exact solutions. We also use linear stability analysis to discuss the instability modulation analysis for stationary solutions. Other partial differential equations can have their exact solutions found using the proposed methodology.</p> </abstract>ARTICLEtrue neural network forecast of PM concentration<abstract> <title style='display:none'>Abstract</title> <p>Particulate Matter 2.5 (PM<sub>2.5</sub>) is a major contributor to air pollution and its exposure has substantial health consequences. As a result, precise prediction of PM<sub>2.5</sub> concentrations is required in order to establish emission reduction strategies for air quality management. The article presents an Artificial Neural Network (ANN) model to forecast PM<sub>2.5</sub> levels in a particular region. The model uses data such as air temperature, carbon monoxide, nitric oxide, nitrogen dioxide, ozone, suspended particles, rainfall, relative humidity, sulfur dioxide, wind direction and wind speed to predict PM<sub>2.5</sub> concentrations in the air accurately. The model’s efficacy is evaluated using statistical measures such as the Coefficient of Determination, the Root Mean Squared Error and the Mean Absolute Error. The study results indicate that the ANN model outperforms more traditional statistical models, with R<sup>2</sup> values of 0.987, which is higher than the values achieved by the Linear Regression and Decision Tree Regressor models, which are 0.88 and 0.89 respectively. The study’s findings have significant implications for public health and environmental policy, as they can provide more accurate and rapid statistics on air quality. The ability to forecast PM<sub>2.5</sub> concentrations can help policymakers and health professionals take proactive measures to mitigate the impact of air pollution on public health.</p> </abstract>ARTICLEtrue generalized Mellin transform and applications to partial and fractional differential equations<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we introduce a generalized Mellin transformation in a general form that encompasses the generalized Mellin transformations found in the literature. Then, we give the fundamental properties of this new integral transformation and apply it to some elementary functions. Furthermore, we obtain the solutions of partial and fractional differential equations by means of this new integral transformation. Finally, we examine the relations between generalized Mellin transformations in the literature and the new generalized Mellin transformation and present a table showing the new integral transformations of functions commonly used in mathematics, physics and engineering applications.</p> </abstract>ARTICLEtrue traveling wave solutions for (2+1)-dimensional Konopelchenko-Dubrovsky equation by using the hyperbolic trigonometric functions methods<abstract> <title style='display:none'>Abstract</title> <p>In this research, the extended rational sinh-cosh method and the modified extended tanh-function method for mathematically constructing traveling wave solutions to the (2+1)-dimensional integro-differential Konopelchenko-Dubrovsky evolution equation are successfully employed to obtain specific appropriate solutions for the first time. A traveling wave transformation was utilized to turn the provided model into a third-order nonlinear ordinary differential equation. Solitary and periodic wave solutions for the model under investigation are obtained in terms of various complex hyperbolic trigonometric and rational functions. Several of the aforementioned solutions have been represented by two- and three-dimensional graphics with appropriate arbitrary parameters to highlight their physical implications. Two-dimensional graphs have presented the influence of time evolution on the solution’s structures.</p> </abstract>ARTICLEtrue study on comparison of pseudorandom number generator<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we have collected some theoretical and practical pseudorandom number generators (PRNGs) with uniform distribution. We have also analyzed some of the most prevalent statistical tests and we present some observations and statistical tests of the sequences generated by the described generators.</p> </abstract>ARTICLEtrue on bipolar cubic fuzzy graphs and its chemical applications<abstract> <title style='display:none'>Abstract</title> <p>In theoretical chemistry, fuzzy molecular graphs can be used to model chemical molecular structures with uncertainty information, where the vertex membership function and edge membership function describe the uncertainty of atoms and chemical bonds respectively. This paper studies chemical topological index of bipolar cubic fuzzy graphs. The new concepts and theorems are given in terms of graph theory and fuzzy set theory approaches and several theoretical conclusions on bipolar Wiener index of bipolar cubic fuzzy graphs are determined. Furthermore, we apply it in chemical science and calculate the bipolar Wiener index of dimethyltryptamine and hallucinogen which are modelled by bipolar cubic fuzzy graphs.</p> </abstract>ARTICLEtrue