Description

Journal of AppliedMath (JAM, eISSN: 2972-4805) is an international, peer-reviewed open access journal that is dedicated to the publication of high-quality research in the field of mathematics. With a commitment to excellence and innovation, JAM provides a platform for mathematicians, scientists, and engineers to share their findings and insights across a broad spectrum of applied mathematical disciplines. It publishes various article types including Original Research Articles, Reviews, Editorials, and Perspectives. Our aim is to encourage scientists to publish their experimental and theoretical results in as much detail as possible. There is no restriction on the length of the papers. At JAM, we believe that thorough research deserves comprehensive presentation. Therefore, we require that the full account of the research be provided, enabling other researchers to reproduce the results. 

JAM is committed to advancing the frontiers of applied mathematics and looks forward to contributing to the global scientific discourse. 

Latest Articles

  • Open Access

    Article

    Article ID: 2176

    On the resolutions of the edge ideals of graphs

    by Margherita Barile

    Journal of AppliedMath, Vol.3, No.2, 2025;

    The so-called bridge-friendliness is a set of divisibility conditions on the minimal generators of monomial ideals. It was introduced by Chau and Kara as a sufficient criterion for the existence of a cellular minimal graded free resolution. It is fulfilled by large classes of monomial ideals, in particular by the edge ideals of acyclic graphs. We present a construction that, given a pair of graphs with bridge-friendly edge ideals, produces a new graph with the same property. An additional assumption is that the starting graphs both have at least one leaf.

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  • Open Access

    Article

    Article ID: 2736

    Mathematical modeling and numerical analysis of diffusion processes in image processing

    by Gargi Trivedi

    Journal of AppliedMath, Vol.3, No.2, 2025;

    This paper introduces a new image enhancement technique based on a revised diffusion model that aims to balance between the reduction of noise and preservation of edges.
    The new model uses adaptive parameters and sophisticated numerical methods to overcome the shortcomings of conventional image processing techniques. This study aims to develop and apply a diffusion model with critical parameters such as the diffusion coefficient, sensitivity parameter, and edge-stopping function parameter. Performance of the model is tested using experiments, comparing with conventional Gaussian smoothing and the Perona-Malik model. Experimental results confirm that the extended diffusion model outperforms the conventional methods on peak signal-to-noise ratio and structural similarity index. The model greatly enhances noise reduction when the parameters are set optimally while preserving significant image details.

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  • Open Access

    Opinion

    Article ID: 2899

    Explicit and accurate solutions for the Benney equation

    by Yuan-Xi Xie

    Journal of AppliedMath, Vol.3, No.2, 2025;

    The Benney equation arises from many different physical contexts as an appropriately real physical model equation involving a lot of effects of dispersion, dissipation, nonlinearity, and instability. As a result, it is a very important and challenging theme to search for the explicit and accurate traveling wave solutions of the Benney equation. In this paper, by introducing an ansatz solution with two E-exponential functions, we have made some improvements to the trial function approach for solving three NPDEs proposed by Xie and Tang. On this basis, we have put forward a direct trial function approach to search for the explicit and accurate traveling wave solutions of NEEs. We have demonstrated its effectiveness by applying it to the Benney equation. Therefore, a series of more general explicit and accurate traveling wave solutions to the Benney equation, comprising the solitary wave solutions and the singular traveling wave solutions, are successfully derived in a forthright and concise way. The obtained results are completely consistent with those given in the existing references. In addition, compared with the proposed approaches in the existing references, the technique described herein seems to be less calculative. Our approach may provide a novel way of thinking for solving NEEs. We firmly believe that the method used herein may also be applied to search for the explicit and accurate traveling wave solutions to other NEEs. We plan to extend this technique to search for the explicit and accurate traveling wave solutions of other NEEs.

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  • Open Access

    Article

    Article ID: 2459

    Fractional optimal control strategies for mitigating cholera epidemics: A mathematical modeling approach

    by Barira Afzal, Muhammad Umar Riaz, Mustafa Habib

    Journal of AppliedMath, Vol.3, No.2, 2025;

    The SIQRB model is employed in this research to propose a Caputo-based fractional derivative optimal control model for the mitigation of cholera epidemics. Significant properties of the model, such as the non-negativity and boundedness of the solution, are verified. The basic reproduction number, , is calculated using the spectral radius of the next-generation matrix. The stability analysis demonstrates that the disease-free equilibrium is locally asymptotically stable when , while the endemic equilibrium is stable when . Numerical simulations are conducted using Euler’s method to demonstrate the importance of the control function. These MATLAB-based simulations illustrate the impact of fractional-order derivatives on cholera transmission dynamics and confirm the analytical results. The efficacy of fractional optimal control approaches in mitigating cholera epidemics is demonstrated.

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  • Open Access

    Article

    Article ID: 1767

    The Jacobsthal-Collatz-Terras model of conjecture the natural numbers in κq + 1 problems

    by Petro Kosobutskyy

    Journal of AppliedMath, Vol.3, No.2, 2025;

    In the work, the unity of the model in both directions of the change of the power of two of the conjecture of natural numbers structured in the form of a set parametrized by a set of odd θ sequences θ × 2 n is justified for the first time. It is shown that the graphs of the direct n(tst) → ∞ and reverse n 0 conjecture of numbers are correctly displayed by the branching diagram of the sequences oriented along the time axis of the full stop of Terrase. The distance between neighbouring nodes is shown to correlate with the Collatz function. The distance δm(p), κ = ακCκq±1 between adjacent nodes is shown to be correlated with the Collatz function. The obtained formula for calculating the period Tκ = ln2(1 + ακκ) according to the degree of formation of powers n. Based on the analysis of regularities of recurrent Jacobsthal numbers and Terras complete stop time, it is shown that the Collatz problem is a partial case of the general Jacobsthal-Collattz-Terrase model of the conjecture of numbers N in both directions of the change of the power of two. Based on this model, the formation of tst{q} sequences was established for numbers with the same lengths as the Collatz sequence CSq.

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  • Open Access

    Article

    Article ID: 2353

    Optimal control of dengue fever transmission dynamics in Kenya

    by Brian Nyanaro, George Kimathi, Mary Wainaina

    Journal of AppliedMath, Vol.3, No.2, 2025;

    The emergence of dengue fever in Kenya has been witnessed in the recent past, leading to public health alerts and disruption of economic activities. The outbreaks have mainly been restricted to the Northeastern and Coastal counties of the country. As such, this paper has focused on an epidemiological model that incorporates an optimal control model of the spread dynamics of dengue fever in Kenya. The objective of the study is to develop an optimal control solution for the spread dynamics of dengue fever in Kenya. This study introduced three time-dependent control variables, which were divided into long-term and short-term control measures. The short-term control measures include prophylactics (treatment) and the use of physical barriers (nets), while the long-term control measure is the treatment of Aedes aegypti mosquitoes with Wolbachia bacteria. The basic reproduction number with the control variables was determined. The set of adjoint points of the control systems was obtained together with the optimal control set. The numerical solutions to the control problem were obtained by use of the forward-backward sweep method and the Runge-Kutta order four method. The impact of utilizing various strategies that employed the combination of the three control measures in different combinations was examined. The control profile of the particular control measures used was also investigated. It was determined that the short-term control measures had more impact on the control of the spread dynamics of dengue fever when compared to the long-term control measure. As such, it was determined that a strategy that incorporates both the long-term and short-term control measures should be utilized for optimum control of dengue fever spread dynamics in Kenya.

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