rss_2.0Sciendo RSS Feed for International Journal of Mathematics and Computer in Engineeringhttps://sciendo.com/journal/IJMCEhttps://www.sciendo.comhttps://sciendo-parsed.s3.eu-central-1.amazonaws.com/676c57637306cc7e8721ea44/cover-image.pnghttps://sciendo.com/journal/IJMCE140216https://sciendo.com/article/10.2478/ijmce-2025-0013<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we reconstruct the gamma and beta functions using a general kernel function in their integral representations. We also reconstruct the Gauss and confluent hypergeometric functions using the beta function with general kernel in their series representations. The general kernel function we use here can be chosen as any special function such as exponential function, Mittag-Leffler function, Wright function, Fox-Wright function, Kummer function or M-series. Using different choices of this general kernel function, various of the generalized gamma, beta, Gauss hypergeometric and confluent hypergeometric functions in the literature can be obtained. In this paper, we first obtain the integral representations, functional relations, summation, derivative and transformation formulas and double Laplace transforms of the special functions we construct. Furthermore, we compute the solutions of some fractional partial differential equations involving special functions with general kernel via the double Laplace transform and graph some of the solutions for specific values. Finally, we obtain the incomplete beta function with general kernel by defining the beta distribution with general kernel.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00132024-09-22T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0015<abstract> <title style='display:none'>Abstract</title> <p>This work effectively utilizes the modified extended tanh− function approach to scientifically deduce semi-analytic traveling wave solutions for the (2+1)-dimensional fourth-order non-linear generalized Hietarinta-type problem, leading to previously unidentified satisfactory solutions. The proposed model has been transformed into a fourth-order non-linear ordinary differential equation via a traveling wave transformation. Some periodic-solitary, original, and oscillating wave solutions to the model under experimentation are acquired in mixed complex trigonometric and logarithmic functions combined with hyperbolic trigonometric functions, and complex rational functions. Assorted solutions have been shown using two- and three-dimensional graphics and suitable arbitrary parameters to demonstrate their physical and dynamic results. Two-dimensional graphs have shown how changes in time formally impact the features and structures of the solution. The free parameters (unrestricted parameters) that keep going in the solutions have a big impact on the dynamic behavior of the solutions. Traveling wave, oscillating, periodic, and breather wave solutions have also been figured out with the help of the operation that gives values to the free parameters.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00152024-09-20T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0020<abstract> <title style='display:none'>Abstract</title> <p>In this paper, constellations of primes are discussed. A number of symmetric prime constellations of even and odd order have been defined and their existence has been computationally verified. Provable minimum extent symmetric constellations have been shown to exist for some cases. Conjectures regarding the existence of higher order symmetric constellations are provided and further areas of research are suggested.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00202024-09-20T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0014<abstract> <title style='display:none'>Abstract</title> <p>This research endeavors to analytically and numerically solve the nonlinear modified Benjamin–Bona–Mahony (mBBM) equation, a model of paramount importance in fluid dynamics, particularly for its application in describing unidirectional water waves with small amplitude that are influenced by dispersion and nonlinear effects. The study’s objective is to enhance the understanding of wave propagation in fluids and to establish a clear connection between the mBBM equation and other nonlinear evolution equations. Utilizing the extended auxiliary equation (EAE) and improved Kudryashov (IKud) methods, the research provides analytical solutions, while the extended cubic–B–spline (ECBS) method validates these solutions numerically. The results showcase the accuracy of the EAE and IKud methods in depicting the wave structures governed by the mBBM equation. The significance of this study lies in its potential to advance the application of the mBBM model in real–world scenarios, such as oceanography and coastal engineering. Conclusively, the research affirms the efficacy of the combined analytical and numerical approach in solving the mBBM equation, contributing novel insights into the field of applied mathematics and nonlinear partial differential equations.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00142024-09-20T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0012<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we study the graph theoretical polynomial known as the Hosoya polynomial obtained from one of the standard classes of graphs called path. Using this polynomial applied for the numerical solution of the nonlinear Fredholm integral equation, which reduces in the algebraic system of equation with collocation points, then solving this system using Newton’s iterative with the help of MATLAB, we obtain the required approximate solution. The desired results in terms of a set of continuous polynomials over a closed interval [0, 1]. Illustrative applications show the efficiency, accuracy and validity of the proposed technique.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00122024-09-19T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0019<abstract> <title style='display:none'>Abstract</title> <p>In the current manuscript, approximate solution for 1D heat conduction equation will be sought with the Septic Hermite Collocation Method (SHCM). To achieve this goal, by means of the roots of both Chebyschev and Legendre polynomials used at the inner collocation points, the pseudo code of the method is found out and applied using Matlab which is one of the widely utilized symbolic programming platforms. The unconditional stability of the scheme is shown by the traditional von-Neumann stability technique. To illustrate the accuracy and effectiveness of this newly current numerical scheme, a comparison among analytical and the computed numerical results is presented in tabular forms. It has been illustrated that the scheme is both accurate and effective one and at the same time can be used in a successful way for finding out numerical solutions of several nonlinear problems as well as linear ones.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00192024-09-19T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0011<abstract> <title style='display:none'>Abstract</title> <p>Alcohol dependence and alcohol abuse are the public health problems. According to World Health Organization data, approximately two billion people in the world consume alcoholic beverages and approximately 77 million people have alcohol use disorder. Epidemiologic studies show that the rate of alcohol dependence varies by region. Fractional derivative models are preferred over integer step models in the control theory of physical, biological, and dynamical systems. Fractional operators are particularly useful in describing the memory and hereditary properties of substances and processes, which are often ignored in integer stepwise derivatives. In this study, we consider a fractional model of alcohol use and analyze its stability. This model is consisted of three compartments: those who do not use alcohol yet but may use alcohol in the future (<italic>S</italic>), those who use alcohol (<italic>A</italic>) and those who quit alcohol for good (<italic>Q</italic>). The fractional derivative is used in the Caputo sense. Mathematical analysis of the fractional <italic>SAQ</italic> model for the mathematical model of alcohol use is performed and numerical results are obtained with the help of the Euler method and graphs are drawn.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00112024-09-19T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0018<abstract> <title style='display:none'>Abstract</title> <p>The ubiquity of smartphones in our daily lives has made them attractive targets for malicious actors seeking to compromise user data and device functionality. Android malware detection has become imperative to protect user privacy and device integrity. This paper presents a focused study on leveraging the Local Outlier Factor (LOF) method for Android malware detection using the DREBIN dataset. Our research addresses the need for accurate and efficient Android malware detection. We explore the LOF method, an anomaly-based detection technique, to assess its effectiveness in distinguishing malicious applications from benign ones within the Android ecosystem. Rigorous experiments using the extensive DREBIN dataset reveal LOF's superiority in accuracy, precision, recall, and False Positive Rate (FPR). We introduce additional metrics like Area Under the Curve (AUC), Matthews Correlation Coefficient (MCC), and True Negative Rate (TNR) to comprehensively evaluate LOF. Our findings highlight LOF's ability to balance false positives and false negatives, making it an ideal choice for Android malware detection. We emphasize the importance of representative datasets, such as DREBIN, for validation. In conclusion, this research positions LOF as a reliable tool for Android malware detection, offering robust protection against emerging threats. As mobile technology evolves, our study encourages further exploration of advanced techniques and real-world deployment scenarios.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00182024-09-18T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0017<abstract> <title style='display:none'>Abstract</title> <p>We have done a theoretical investigation into the propagation of nonlinear dust ion acoustic solitary waves and their soliton properties in a three-component magnetized collisionless plasma consisting of inertial positively charged ions, noninertial electrons following a Tsallis <italic>q</italic>–distribution, and stationary negatively charged dust grains. We consider a uniform external magnetic field along the <italic>z</italic>–direction, and the wave propagation occurs obliquely to the magnetic field direction. It is observed that the two types of wave modes namely slow and fast modes, are appears in the linear analysis. By employing the reductive perturbation method, the Korteweg-de Vries (KdV) and modified KdV equations are determined to describe the small amplitude dust ion acoustic soliton. The dependence of several physical plasma parameters including nonextensive <italic>q</italic>–parameter, magnetic field strength <italic>etc.</italic> of our plasma on the propagating dust ion acoustic solitary waves potential are numerically examined. This study shows the simultaneous existence of compressive and rarefactive solitons due to the variation of first order nonlinearity coefficient represented by the KdV equation and it is found that there is a critical point for the plasma parameters where the amplitude of the soliton of KdV equation become diverges. The mKdV equation with second order nonlinearity coefficient is derived from there and observed the solitons only with finite amplitude. The present study could be helpful for understanding the nonlinear travelling waves propagating in laboratory and space plasma environments.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00172024-09-18T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0016<abstract> <title style='display:none'>Abstract</title> <p>This study investigates the thermohaline convection in MHD Casson fluid over an exponentially stretching sheet. This study has practical significance in industrial processes, materials processing, energy systems, and environmental applications. The governing equations describing the conservation for an electrically conducting fluid flow, thermal and concentration transports are considered based on the principles of mass, momentum, energy and concentration equations. Our first step involves transforming the governing nonlinear partial differential equations into a coupled nonlinear ordinary differential equations with the help of suitable similarity transformations. Second step, infinite domain [0, ∞) of the problem to a finite domain [0, 1] through a coordinate transformations. This specific choice is motivated by the wavelet's significance in the finite domain of [0, 1]. Third step, we effectively solve the resulting coupled nonlinear ordinary differential equations using the numerical Hermite wavelet method (HWM). This approach proves to be a valuable technique for obtaining significant results and insights in our study. Finally, the effect of known physical parameters on velocity, temperature and concentration are analysed through tables and graphs.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00162024-09-18T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0010<abstract> <title style='display:none'>Abstract</title> <p>This article describes an approach known as the conjugate Gram-Schmidt method for estimating gradients and Hessian using function evaluations and difference quotients, and uses the Gram-Schmidt conjugate direction algorithm to minimize functions and compares it to other techniques for solving ∇<italic>f</italic> = 0. Comparable minimization algorithms are also used to demonstrate convergence rates using quotient and root convergence factors, as described by Ortega and Rheinbolt to determine the optimal minimization technique to obtain results similar to the Newton method, between the Gram-Schmidt approach and other minimizing approaches. A survey of the existing literature in order to compare Hestenes’ Gram-Schmidt conjugate direction approach without derivative to other minimization methods is conducted and further analytical and computational details are provided.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00102024-06-03T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0009<abstract> <title style='display:none'>Abstract</title> <p>Square is one of the basic arithmetic operations. Referring to the earlier contributions provided by ancient Indian mathematicians concerning square calculation, various techniques have been suggested by Arybhata, Bhaskara I, Sridhara, Mahavira and Bhaskara II to quote a few. Besides, P. Swami Bharati Krishna Tirthji discussed various techniques for square calculating based on various sutras. In this paper, we summarise the works done by ancient Indian mathematicians and discuss the applications of calculating squares using different sutras. In addition, we propose a new method of calculating square based on the drawbacks identified and that can be applied for the square calculation of any number. Our method splits the number and hence makes the calculation simpler. Moreover, for bigger values, nested calculations can also be applied.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00092024-06-03T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0008<abstract> <title style='display:none'>Abstract</title> <p>In this paper, the main objective is to demonstrate the existence of solutions for an equation resembling the Cahn-Hilliard model, featuring a proliferation term and a logarithmic nonlinear term. This equation is conceptualized within the context of interactions in liquid-gas systems, particularly in the context of island formation. The primary challenge lies in the departure from the original Cahn-Hilliard equation, as we no longer maintain conservation of the spatial average mean of the order parameter. This departure introduces the complexity in establishing uniform estimates for the solutions of the approximated problems concerning the regularization parameter, as it may potentially result in finite-time blow-up.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00082024-06-02T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0002<abstract> <title style='display:none'>Abstract</title> <p>This work is on a fuzzy initial value problem with fuzzy coefficient. The problem is investigated via fuzzy Laplace transform method under generalized differentiability. The solutions of the problem are thus found. The problem is illustrated with an example. Using the generalized differentiability, solutions of a fuzzy initial value problem with fuzzy coefficient are investigated via fuzzy Laplace transform method. The graphics of the solutions are drawn. Conclusions are given.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00022024-06-02T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0001<abstract> <title style='display:none'>Abstract</title> <p>The Fokas-Lenells model has broad applications in nonlinear physics when studying various soliton phenomena. Employing the direct algebraic scheme, the modified rational sine-cosine technique, and the (1/<italic>G′</italic>) expansion scheme, the analytical solutions to this model are derived. Double periodic waves, bright soliton, dark soliton, single and multiple breather waves, and periodic breather waves are extracted from this model using symbolic computation. The dynamic behaviors of the acquired outcomes are vividly illustrated through density, two-dimensional (2D), and three-dimensional (3D) graphical representations. These discoveries are strategically positioned to significantly contribute to the advancement in the exploration of nonlinear models, standing as a fundamental pillar for forthcoming research endeavors.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00012024-06-02T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0006<abstract> <title style='display:none'>Abstract</title> <p>Numerical simulations of an unsteady laminar lid-driven cavity Newtonian flow are executed to demonstrate the formation of eddies under different aspect ratios and steady-state criteria. A couple of nonlinear unsteady partial differential equations (PDEs) of Navier Stokes satisfying a set of boundary conditions is examined with both inclusions of no-slip and free-slip effects. Finite difference method (FDM) is employed to solve the vorticity-stream function using a self-developed Matlab_® code embedded in a Graphical User Interface (GUI) to ease the cavity problem analysis by the end users. Four models are studied where Ansys Fluent_® employing the Finite Element Method (FEM) is used to verify the present FDM steady-state results produced for the first model. It is observed that the value of stream function begins to drop and streamline distribution changes shape when <italic>e</italic> ≤ 10⁻⁵. Refrainment of merging of secondary eddies also happens when the free-slip boundary condition effect passes the threshold value. The Stretching effect with free-slip BC in the fourth model regulates the fluid dynamics to reach the entire cavity sufficiently with no room for eddy formation by increasing the slip length to an intense value. Free-slip simulates free surface applications in geophysical occurrences (river and glacier), spilling dynamics, ship hull designs, technologies of coating and fuel spraying/injection.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00062024-06-02T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0003<abstract> <title style='display:none'>Abstract</title> <p>This study delves into the exploration of three distinct envelope solitons within the nonlinear dispersive modified Benjamin Bona Mahony (NDMBBM) equation, originating from seismic sea waves, and the Kudryashov-Sinelshchikov (KS) equation. The solitons emerge naturally during the derivation process, and their existence is scrutinized using the ansatz approach. The findings reveal the presence of non-topological (bright), topological (dark) solitons, and rogue wave (singular) solitons, presenting significant applications in applied research and engineering. Additionally, two-dimensional and three-dimensional revolution plots are employed with varying parameter values to scrutinize the physical characteristics of these solitons.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00032024-06-02T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0007<abstract> <title style='display:none'>Abstract</title> <p>One of the most important fluid flows is blood flow seen in hemodynamics, which is a vital process and carries many components from one place to another in the interior of the body. Blood is a special suspension; it is a non-Newtonian fluid as the blood flow cannot be compressed due to the imbalance in strain force and velocity. Blood flow is modelled by various equations which are based on fundamental equations such as the Korteweg-De Vries (KdV) equation and the nonlinear Schrödinger type equations. In this study, some new solitary solutions of the blood flow models are obtained in explicit form via the Bernoulli method which is one of the ansatz-based methods. Moreover, 3D and 2D simulations under the suitable values of the parameters of the solutions obtained are plotted.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00072024-06-02T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0005<abstract> <title style='display:none'>Abstract</title> <p>Identifying vulnerabilities within source code remains paramount in assuring software quality and security. This study introduces a refined semi-supervised learning methodology that capitalizes on pattern-exploiting training coupled with cloze-style interrogation techniques. The research strategy employed involves the training of a linguistic model on the Software Assurance Reference Dataset (SARD) and Devign datasets, which are replete with vulnerable code fragments. The training procedure entails obscuring specific segments of the code and subsequently prompting the model to ascertain the obfuscated tokens. Empirical analyses underscore the efficacy of our method in pinpointing vulnerabilities in source code, benefiting substantially from patterns discerned within the code fragments. This investigation underscores the potential of integrating pattern-exploiting training and cloze-based queries to enhance the precision of vulnerability detection within source code.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00052024-06-02T00:00:00.000+00:00https://sciendo.com/article/10.2478/ijmce-2025-0004<abstract> <title style='display:none'>Abstract</title> <p>This study presents a mathematical model to investigate the dynamics of Human Immunodeficiency Virus infection and Acquired Immunodeficiency Syndrome (HIV/AIDS) transmission. Employing mathematical analysis, non-negativity, boundedness, the basic reproduction number <italic>ℛ</italic>₀, and the stability of both the disease-free and endemic equilibrium of the proposed model were derived. Normalized forward sensitivity techniques are used to determine the significance and importance of sensitive parameters associated with <italic>ℛ</italic>₀. To gain insights into the dynamical behavior of each compartment, an effective numerical scheme was utilized, and the results obtained suggest that there is a need, even if individuals are infected with the virus, to use non-pharmaceutical interventions as control strategies.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/ijmce-2025-00042024-06-02T00:00:00.000+00:00en-us-1