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        <title>International Journal of Mathematics and Computer in Engineering Feed</title>
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            <title>International Journal of Mathematics and Computer in Engineering Feed</title>
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        <copyright>All rights reserved 2026, Harran University</copyright>
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        <item>
            <title><![CDATA[Directional migration and competition in fluid media: Global existence, uniqueness, and robust simulation of chemotaxis and tumor growth dynamics]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0018</link>
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            <pubDate>Tue, 02 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

Unlike classical isotropic models, this work establishes a mathematical framework for analyzing interspecies competition in fluid environments with nonlinear degenerate anisotropic diffusive fluxes, a setting that has not been rigorously treated before. The first major novelty is a rigorous proof of the global existence of weak solutions, despite the strong nonlinearity and degeneracy of the operators. Furthermore, we provide one of the first uniqueness results for weak solutions under Stokes coupling, obtained via a carefully tailored duality method. On the computational side, we generalize a convergent hybrid finite volume-finite element scheme that overcomes the traditional instability and mesh-dependence issues plaguing anisotropic systems. This scheme guarantees confinement properties consistent with biological admissibility and is implemented in a robust predictive solver. Numerical experiments conducted on heterogeneous domains reveal new classes of dynamical behaviors in two-species systems, including anisotropy-driven spatial segregation and complex domains. By integrating analytical rigor and advanced numerics, this study provides a novel benchmark for the well-posedness and simulation of nonlinear anisotropic ecological and biomedical systems, with particular relevance to tumor growth dynamics and multi-species chemotaxis competitive systems.
]]></description>
            <category>ARTICLE</category>
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        <item>
            <title><![CDATA[Reduction to a Fredholm integral equation and numerical solution of the inverse Cauchy problem for the Schrödinger-Pauli equation]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0015</link>
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            <pubDate>Tue, 02 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

This paper studies the inverse Cauchy problem for the two-dimensional Schrödinger-Pauli equation, which models a spin-12{1 \over 2} quantum particle in a magnetic field. The problem involves reconstructing an inaccessible boundary condition from overdetermined data, a severely ill-posed inverse problem. We develop a numerical method combining Lavrentiev regularization with Haar wavelet discretization, yielding a regularized Fredholm equation solved via an efficient collocation scheme with explicit matrix entries. Numerical results demonstrate first-order convergence and robustness to noise up to 10%. Notably, multi-frequency solutions exhibit enhanced noise stability compared to single-mode cases. The method provides a stable, efficient framework for boundary reconstruction in quantum systems with partial data.
]]></description>
            <category>ARTICLE</category>
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        <item>
            <title><![CDATA[Further characteristics for certain newly formed solutions for two significant mathematical models by utilization of an efficient semi-analytic method ]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0022</link>
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            <pubDate>Tue, 02 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

This study analyses the details of two mathematical models: the (2+1)-dimensional nonlinear time-fractional HirotaMaccari (HM) model, which includes a novel fractional operator called the β-derivative, and the (3+1)-dimensional Korteweg-de Vries-type equation. Two different forms of the wave transformations are utilized to convert the studied models into nonlinear differential equations. The improved version of the generalized Kudryashov method (IGKhM), known for its efficiency, is applied for the first time to investigate models studied. Various computational programs provide essential visual representations, making them invaluable in academic and practical applications. The construction of traveling waves and singular solitons is achieved using exponential and hyperbolic trigonometric functions, which exhibit characteristics of darkness, brightness, and mixed states. In two- and three-dimensional representations, numerical simulations of the outcomes are incorporated to better express and understand the physical significance of the results. Every solution obtained is new and distinctive compared to previous studies. Additionally, the results are individually substituted into the corresponding equations and satisfy the conditions.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[A large language model-based analysis of vulnerability discovery in windows software]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0019</link>
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            <pubDate>Tue, 02 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

Source code security auditing is essential before software release in order to identify programming faults that may lead to vulnerabilities and functional failures. In this paper, we present a structured security assessment of the Windows App SDK by integrating multiple static analysis tools with a context-aware and disagreement-aware Large Language Model (LLM) interpretation layer. Although static analyzers are effective in reporting potential weaknesses, their raw outputs often contain redundant alerts, limited contextual explanation, and inconsistent severity assignments. To address these limitations, the proposed LLM-based interpretation layer normalizes and de-duplicates alerts, filters context-limited or nonactionable warnings, and refines severity prioritization under inter-tool disagreement without introducing new vulnerability discoveries. Experimental results show the security findings before and after LLM-based interpretation. In particular, the proposed framework reduces static-analysis alerts by 62.5%. In addition, disagreement-aware severity refinement eliminates over-prioritized critical findings and improves prioritization by reducing Medium findings from 11 to 7 and Low findings from 42 to 28. These results demonstrate the potential of LLM-based interpretation to reduce noise in static-analysis outputs and improve vulnerability prioritization for practical security assessment.
]]></description>
            <category>ARTICLE</category>
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        <item>
            <title><![CDATA[Application of machine learning frameworks in the controllability study of infinite-delay neutral integro-differential equations]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0021</link>
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            <pubDate>Tue, 02 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

The article delves into the controllability of second-order neutral functional integro-differential systems with infinite delay, which is a combination of neutrality, memory effects, and integral terms causing significant analytical challenges. We focus on the stochastic approach and the random fixed point theorem for set-valued operators to show that mild random solutions exist and also how randomness can make the problem easier. We then present rigorous controllability results, which are complicated by the presence of unbounded delay and impulsive effects. Theoretical contributions aside, the paper also demonstrates the use of such controllable systems to generate reliable simulated trajectories that are supportive of data-driven applications such as neural-network-based forecasting models. Thus, the integration confirms the practical relevance of the developed theory and its potential to solve real-world problems via advanced mathematical modeling. The primary objective of this study is to establish existence and controllability results for such systems within a unified stochastic framework. Using a random fixed-point theorem for set-valued operators, sufficient conditions for the existence of mild random solutions and controllability are derived. The novelty of the work lies in the combined treatment of infinite delay, neutrality, impulsive effects, and stochastic perturbations, together with its application to data-driven and machine-learning-based modeling.
]]></description>
            <category>ARTICLE</category>
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        <item>
            <title><![CDATA[Dynamics of solitons, multi-lumps, and their interactions of the Konopelchenko-Dubrovsky-Kaup-Kupershmidt and Bogoyavlensky-Konopelchenko model in (3+1)-dimensions using the modern advanced approach]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0017</link>
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            <pubDate>Tue, 02 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

In this original research, we explore new forms of soliton solutions, lumps, and the dynamics of water waves of the considered Generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (KDKK) and Bogoyavlensky-Konopelchenko (BK) equations in (3+1)-dimensions, utilizing the Hirota bilinear approach. We apply the Painlevé analysis to check the integrability of this model. We formulate a bilinear equation in an auxiliary function using the Cole-Hopf transformation and then develop it into a Hirota bilinear form using a bilinear differential operator. Based on this technique, we derive lump waves, breaking phenomena, solitons, peakons, wave interactions, and wave-to-wave collisions. The solutions are obtained using ansatz functions in quadratic, sine, cosine, and exponential functions. We also illustrate how the lump interacts with solitary, periodic, and breather waves to generate various dynamics of water waves in the obtained solutions, which are visualized graphically via 2D, 3D, and contour plots with the help of symbolic software Maple. We also show the phase plane portraits, bifurcation analysis, and sensitivity analysis based on the bifurcation method with the help of the equilibrium points of the governing model studied.
]]></description>
            <category>ARTICLE</category>
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        <item>
            <title><![CDATA[Groundwater depletion: A mathematical model incorporating climate and human factors]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0016</link>
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            <pubDate>Tue, 02 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

Groundwater is vital for ecological balance and human use but is increasingly affected by factors such as pollution, excessive water consumption, and deforestation. We develop an advanced ordinary differential equation (ODE) model that includes new terms reflecting interactions between atmospheric water, surface water, and groundwater. This model incorporates various parameters for pollution, frequent water pumping, and deforestation, and examines how these factors influence groundwater dynamics. To investigate the system’s behavior, we conduct a detailed analysis of equilibrium points and their stability. The model is further validated through numerical simulations by using the Runge-Kutta 4th order (RK4) method, which reveal the influence of various stressors on groundwater sustainability. This approach enhances understanding of groundwater interactions and supports better resource management strategies.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Modeling Crimean-Congo Hemorrhagic fever with behavioral awareness: Mathematical analysis via Chebyshev spectral collocation solutions]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0020</link>
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            <pubDate>Tue, 02 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

We develop a deterministic awareness-driven compartmental model for the transmission dynamics of Crimean-Congo Hemorrhagic Fever (CCHF), incorporating vector-mediated infection, zoonotic spillover, limited human-to-human transmission, and awareness-induced behavioral responses. The well-posedness of the model is established by proving positivity and boundedness of solutions. The basic reproduction number ℛ0 is derived via the next-generation matrix approach, and the local stability of the disease-free equilibrium is analysed and shown to be governed by this threshold. A sensitivity analysis has been performed to validate the most significant parameters. To solve the resulting nonlinear system accurately over extended time horizons, a high-order numerical framework is constructed by coupling the quasilinearization method with Chebyshev spectral collocation and a domain decomposition strategy. Convergence and spectral accuracy of the proposed scheme are established rigorously. Numerical simulations validate the theoretical findings and demonstrate the effectiveness of awareness-based interventions in reducing disease burden.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[The future of web application security: Opportunities and challenges for machine learning-based techniques]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0002</link>
            <guid isPermaLink="false">https://sciendo.com/article/10.2478/ijmce-2026-0002</guid>
            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

In this paper, the future prospects and potential for machine learning-based solutions in web application security are examined. These include enhancing accuracy and efficiency, real-time detection, scaling, explainable Artificial Intelligence (AI), adversarial machine learning, and automated response. The article also gives a general overview of Machine Learning (ML) methods that are frequently applied to web application security, including supervised learning methods like decision trees, Support Vector Machines (SVMs), and neural networks, unsupervised learning methods like k-means clustering and Principal Component Analysis (PCA), and deep learning methods such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs). The incorporation of machine learning-based approaches into security measures will be more necessary as online applications continue to develop in order to meet new threats.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[A mathematical model of HPA axis dynamics and impacts of alcohol consumption]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0006</link>
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            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

In this study, we develop a mathematical model to examine the effects of varying levels of alcohol consumption on the dynamics of the hypothalamic-pituitary-adrenal (HPA) axis. Our model also integrates circadian and ultradian rhythms to more accurately represent physiological responses over time and explores age and gender related impacts on HPA axis function. Despite the omission of gonadal hormone-cortisol interactions and other simplifying assumptions that had minimal influence on outcomes, simulation results reveal a significant association between elevated alcohol intake and the development of hypercortisolism, or Cushing’s syndrome, underscoring potential disruptions in HPA axis function and circadian rhythm behavior induced by alcohol. These findings underscore the importance of understanding the influence of external factors such as alcohol on stress regulation and provide new insights into the pathophysiology of stress-related disorders.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[A new application of Taylor expansion for approximate solution of systems of Fredholm integral equations]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0008</link>
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            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

Systems of Fredholm integral equations are essential in engineering fields for modeling complex systems involving dynamic behavior, material properties, and interactions between different forces or fluids. In this research, the Taylor expansion approach is used to solve the systems of linear Fredholm integral equations (SLFIEs) of the second kind in a novel manner. By combining the mth-order Taylor polynomial of unknown functions at an arbitrary point and employing the repeated integration method; the given system of linear Fredholm integral equations is transformed into a new system of linear equations of unknown functions and their derivatives. Eventually, this new system is solved to obtain demanded mth-order approximate solutions. An error analysis is given as well as several numerical examples to demonstrate the efficiency, accuracy, and ability of the proposed method. Furthermore, this method always leads to the exact solution if the exact solution is a polynomial of degree less than or equal to m.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Signless Laplacian spectrum of power graph of certain finite non-commutative groups]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0003</link>
            <guid isPermaLink="false">https://sciendo.com/article/10.2478/ijmce-2026-0003</guid>
            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

In this study, we investigate the signless Laplacian spectrum of power graphs of different finite non-commutative groups. Initially, we obtain the spectrum of the signless Laplacian matrix of power graph of elementary abelian groups whose orders are powers of a prime number. The signless Laplacian spectrum of the smallest sporadic group, the Mathieu group M11, is then computed. We also find the signless Laplacian eigenvalues of 𝒫(Q2k+2), where Q2k+2 represents the generalized quaternion group. For 𝒫(Dic4n), where Dic4n is the dicyclic group, we finally give bounds on the signless Laplacian spectral radius.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[A study on different classes of differential equations by semi-analytical and numerical techniques]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0004</link>
            <guid isPermaLink="false">https://sciendo.com/article/10.2478/ijmce-2026-0004</guid>
            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

This study applies the Homotopy analysis method (HAM) and Haar wavelet transform (HWT) in order to provide an innovative technique for approximating to the nonlinear ordinary differential equations (ODEs), a system of ODEs, and partial differential equations (PDEs). HAM is a potent semi-analytical method that works well when studying linear and nonlinear problems. HWT is a numerical technique that effectively discretizes differential equations (DEs) simultaneously. A robust analytical method builds a family of equations that smoothly transforms the original nonlinear equation into a straightforward linear issue using the topological concept of homotopy. This allows the derivation of extremely precise series solutions. Real-world application problems are solved to analyze the correctness and effectiveness of the projected system.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[A robust framework for solving PDEs: Biorthogonal spline wavelet methods]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0005</link>
            <guid isPermaLink="false">https://sciendo.com/article/10.2478/ijmce-2026-0005</guid>
            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

This paper presents a new numerical approach for solving the partial differential equations (PDEs), focusing on the Diffusion equation. The method combines a collocation approach with wavelet techniques to achieve high accuracy in approximating solutions. A detailed framework for the proposed method, explaining the discretization process at multiple collocation points and the formulation of the resulting system of linear equations is provided. An implementation is conducted to demonstrate the method’s effectiveness in capturing the complex behaviors typical of the model studied. Comparisons with analytical solutions underscore the robustness and precision of the technique, paving the way for its application in diverse fields such as physics, finance, and engineering.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[On the soliton solutions of the generalized stochastic nonlinear Schrödinger equation with Kerr effect and higher order nonlinearity via two analytical methods]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0007</link>
            <guid isPermaLink="false">https://sciendo.com/article/10.2478/ijmce-2026-0007</guid>
            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

In this study, we investigate the generalized stochastic nonlinear Schrödinger equation, which models the propagation of ultra-short optical pulses in nonlinear and dispersive media, incorporating both the Kerr effect and higher-order nonlinearities. In order to construct exact analytical solutions, we employ the tan(ϖ(ξ)2)tan(\frac{\varpi(\xi)}{2})-expansion method and the (G’/G,1/G)-expansion method. These methods yield a variety of exact solutions, including dark, singular, and singular periodic soliton solutions, each representing different physical wave behaviors. We further perform a stability analysis to determine the robustness of these solutions under perturbations and examine their temporal evolution to better understand their propagation dynamics. Graphical illustrations of selected solutions are provided to visualize their dynamics and to demonstrate how the passage of time influences the structure and stability of the resulting wave forms.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Dynamics of new truncated M-fractional derivative wave structures to the nonlinear Zhiber-Shabat equation arising in variety of fields]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0009</link>
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            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

In this work, we explore the different wave structures and the effect of fractional parameter on the nonlinear partial differential equation known as the nonlinear Zhiber-Shabat equation (ZSE). This model has a variety of applications in the mathematical community, including fluid dynamics, integral quantum field theory, nonlinear optics. The recently developed integration techniques known as generalized Riccati equation mapping method, the Kumar-Malik method (KMM) and multivariate generalized exponential integral function approach are adopted. The suggested model is transformed into a nonlinear ordinary differential equation with the application of the truncated M-fractional derivative in order to get the intended results. The obtained structures are novel and expressed in the form of solitary wave solutions including hyperbolic, periodic as well as exponential function solutions under certain conditions. Various combinations and magnitudes of the physical parameters are employed to investigate the soliton solutions of the resultant system. Graphs are constructed by plotting the final solutions with the appropriate parameter values to elucidate the scientific interpretation and physical importance of the analytical findings.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Experimentally optimizing a spinning disk by manipulating its mass distribution and radius]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0010</link>
            <guid isPermaLink="false">https://sciendo.com/article/10.2478/ijmce-2026-0010</guid>
            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

The scientific method enables the experimental study of complex phenomena by isolating key variables. This work explores the significant properties of spinning bodies. Optimizing spinning disks is the primary aim of this work. Optimization is achieved by manipulating the moment of inertia (MOI) of the disk, allowing a longer duration of spin and lowering the rate of energy dissipation. Experiments are designed and conducted to explore the relationship between the radius and mass distribution of the disk and the angular deceleration experienced by it. Effects of the same on energy retention is analyzed. Empirical data is interpreted graphically while accounting for systematic and random uncertainties. Percentage change in duration of spin as a result of percentage change in physical quantities is studied. Moving mass away from the central axis of the spinning disk increases its duration of spin from a constant initial angular velocity. Energy retention is also improved. Increasing the radius of the disk increases the duration of spin and reduces the rate of energy dissipation. The above conclusions are drawn from experiments where the mass and thickness of the disk are controlled along with other necessary factors that can influence the results. The experiments confirm the existing theory relating to the moment of inertia, angular quantities, resistive torques and kinetic energy of spinning disks. The experiments provide insights into the behavior of spinning disks in practical situations, especially in problems concerned with optimization in the field of mechanical engineering.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[On the rational sine-Gordon solution of the forced KdV equation]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0001</link>
            <guid isPermaLink="false">https://sciendo.com/article/10.2478/ijmce-2026-0001</guid>
            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

The KdV equation with a forcing term is solved by searching the sine-Gordon solution. The KdV equation is converted into a nonlinear ordinary differential equation (NODE). The analytical solutions of the model studied is obtained in terms of some suitable periodic functions. The physical meanings of the parametric dependence of solutions is also studied.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[A neural network process for the fractional order lungs cancer operation system]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0011</link>
            <guid isPermaLink="false">https://sciendo.com/article/10.2478/ijmce-2026-0011</guid>
            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

The purpose of current research is to provide the solutions of the fractional lungs cancer operation system using one of the neural network approaches. The mathematical model is divided into immune/epithelial cells, tumor suppressor genetic factor, evolution factor oncogenes, and blood lung cancer vessels. The fractional derivatives are performed more competently as compared to integer order derivatives. A neural network approach based on the Levenberg-Marquardt Backpropagation is applied to solve the fractional kind of derivative to have the solution of the system. Eighteen numbers of neurons along with sigmoid activation function in the hidden layer are used in the neural network process, while the data is created via Adam numerical solver with the selection of different percentages including testing, training and verification. The correctness of the designed neural network scheme is observed through the matching of the outcomes, best training performances and insignificant absolute error. Moreover, some tests based regression, state transition, and error histogram are also been used to check the validity of the proposed scheme.
]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[An efficient higher-order trigonometric cubic B-spline collocation method for time-fractional Burgers equations]]></title>
            <link>https://sciendo.com/article/10.2478/ijmce-2026-0013</link>
            <guid isPermaLink="false">https://sciendo.com/article/10.2478/ijmce-2026-0013</guid>
            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[

This manuscript is devoted to investigate the numerical solutions of the nonlinear time-fractional Burgers equation representing a significant extension of the classical Burgers equation to fractional derivative. For this purpose, an efficient higher-order trigonometric cubic B-spline collocation method, which is based on finite element analysis, is presented and used to achieve the aim of this work. While obtaining the numerical solutions of the mentioned equation, the discretization of the spatial part is performed via the Crank-Nicolson approach and the time derivative is performed in Caputo sense and the discretization of the time derivative is made by L1 algorithm. Also, the nonlinear term seen in the Burgers equation is linearized through the use of the Rubin-Graves linearization technique. Consequently, the performing of the collocation method is resulted to obtain a numerical scheme which is producing an algebraic system being solved by iteratively. The stability of the numerical scheme is investigated using the von-Neumann stability criteria. Three test problems are considered to confirm the validity, accuracy and efficiency of the method. The error between numerical solutions and exact ones is measured with the norms L2 and L∞ Comparison results are presented by tables, the behaviour of the numerical solutions and the harmony with the exact solutions are depicted with graphs as well.
]]></description>
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