Papers by Journal of Mathematics and Computer Science (JMCS)
Journal of Mathematics and Computer Science, 2026
This study focuses on applying the Lie symmetry method, to obtain exact solutions in multiple for... more This study focuses on applying the Lie symmetry method, to obtain exact solutions in multiple forms for the (3 + 1)dimensional (3D) heat model This equation is a well-known model frequently used to describe numerous complex physical phenomena. Initially, the geometric vector fields for the 3D heat-type equation are determined. Using Lie symmetry reduction, we report a wide array of exact analytical solutions that encompass trigonometric and hyperbolic solitons, Lambert functions, polynomials, exponential and inverse functions, hypergeometric forms, Bessel functions, logarithmic forms, rational forms, and solitary wave solutions. These solutions include many rational forms that uncover intricate physical structures that have not been previously reported. The solutions presented in this study are original and significantly distinct from previous findings. They have significant potential for application in diverse fields, including fiber optics, plasma physics, soliton dynamics, fluid dynamics, mathematical physics, and other applied sciences. The findings demonstrated that these mathematical techniques are efficient, straightforward, and robust, making them suitable for solving other types of nonlinear equations.
Journal of Mathematics and Computer Science, 2026
According to the World Health Organization's guidelines, a two-year breastfeeding period is stron... more According to the World Health Organization's guidelines, a two-year breastfeeding period is strongly recommended, with research demonstrating its significant benefits in reducing childhood illnesses and mortality rates. Acknowledging this evidence, this study aims to explore this recommendation by focusing on a specific infection, namely Hand, Foot, and Mouth Disease (HFMD). We do so by extending and analyzing an SEIR epidemic model uniquely designed for HFMD transmission and how it affects regional residency in Thailand. The proposed model examines two equilibria: disease-free and endemic, revealing local and global stability conditions determined by the basic reproduction number (R bfeed). Our analysis includes global stability for both disease-free and endemic equilibrium points, using a quadratic Lyapunov function for the global stability assessment of the endemic point. Additionally, we conducted a sensitivity analysis of different parameters for the basic reproduction number to enhance our understanding of model dynamics. Finally, numerical simulations, which include the simulation of general dynamics, examining the impact of breastfeeding, data fitting, model validation, and predicting future HFMD forecasts, were conducted using RStudio and Python software. These simulations help us explore the effects of breastfeeding on HFMD transmission, offering insights into the potential implications for controlling hand, foot, and mouth disease among children in Thailand.
Journal of Mathematics and Computer Science, 2026
The dynamic interplay between the tumor and the immune system determines if cancer advances or re... more The dynamic interplay between the tumor and the immune system determines if cancer advances or retreats. This study investigates a three-dimensional nonlinear differential system incorporating tumor cells, hunting CTLs, and resting CTLs under the Caputo-Fabrizio fractional derivative framework. The complex and dynamic interaction between immune cells and tumor cells plays a crucial role in the development, progression, and treatment of cancer. Key dynamical aspects, such as the existence and uniqueness of solutions, equilibrium points, and their stability, are rigorously analyzed. To bridge theory with practical validation, circuit implementations are developed using MATLAB, enabling the comparison of computational precision and authenticity for the tumor model. This innovative approach highlights how circuit-based representations can enhance the understanding of tumor-immune dynamics, which further helps in the treatment of cancer. Numerical simulations, incorporating estimated parameter values, validate the theoretical findings and provide deeper insights into the system's behavior. These results contribute to a more comprehensive understanding of tumor progression and immune response modulation, paving the way for improved strategies in cancer treatment.
Journal of Mathematics and Computer Science, 2026
This article establishes novel fixed point theorems for Ψ-orbitally continuous mappings in b-metr... more This article establishes novel fixed point theorems for Ψ-orbitally continuous mappings in b-metric spaces, extending the foundational results. The findings are applied to demonstrate the existence and uniqueness solutions for nonlinear integral equations and analyzing the stability of neural networks.
Journal of Mathematics and Computer Science, 2026
The aim of this paper is to propose Krasnosel'skii-Mann type iteration with double inertial steps... more The aim of this paper is to propose Krasnosel'skii-Mann type iteration with double inertial steps for approximating fixed points of nonexpansive mappings in real Hilbert spaces. The weak convergence is proved under some suitable conditions of the parameters. Some applications to the problems of finding a common fixed point of a family of mappings are also given. Finally, several numerical experiments to show the efficiency and accuracy of our method in breast and cervical cancer diseases predictions are presented.
Journal of Mathematics and Computer Science, 2026
The objective of this paper is to propose a novel incremental proximal algorithm that incorporate... more The objective of this paper is to propose a novel incremental proximal algorithm that incorporates gradient penalization strategies within a fixed-point framework for solving convex bilevel optimization problems. The outer-level objective is modeled as the sum of two composite convex functions, one of which is nonsmooth. We establish a convergence theorem for the proposed algorithm under suitable assumptions. Additionally, we provide numerical experiments to demonstrate the effectiveness of the method in solving image inpainting problems. Comparative results with existing algorithms in the literature indicate that the proposed approach exhibits superior convergence performance.
Journal of Mathematics and Computer Science, 2026
The delay differential equations (DDEs) are widely used to explore various engineering and physic... more The delay differential equations (DDEs) are widely used to explore various engineering and physical applications. An example of DDEs with proportional delays is known as the pantograph model which governs the current collection in electric trains. DDEs with constant delays also have different applications. This paper introduces a unified approach to analyze a class of first order DDEs under arbitrary history functions (HFs). The proposed approach assumes that the arbitrary HF ϕ(t) can be represented as Maclaurin series with coefficients ϕ m , m ⩾ 0. Based on this assumption, the solution in each sub-interval of the problem's domain is obtained in explicit form in terms of the coefficients ϕ m. Exact solutions are obtained for several examples subjected to history functions of different forms. Properties of the solution and its derivative are proved and examined theoretically. Existing results in the literature are derived from the current ones as special cases. In view of the obtained results, the exact solution of any first order linear delay differential equation can be directly determined once the coefficients ϕ m of the given history function is inserted into the standard solution. This reflects the advantage of the proposed approach over other techniques. Moreover, the suggested analysis can be easily extended to include higher order linear delay models.
Journal of Mathematics and Computer Science, 2026
This paper investigates a new category of a fractional boundary value problem (BVP) involving the... more This paper investigates a new category of a fractional boundary value problem (BVP) involving the generalized Atangana-Baleanu-Caputo (ABC) derivatives of order belonging to (2, 3]. First, the Green function with its properties for a proposed fractional BVP are derived. Then, the theoretical results are established by various techniques. The existence and uniqueness of theorems of the solutions are proved by utilizing the Weissinger, the Aghajani fixed point theorems, the Meir-Keeler condensing operator, and the Kuratowski's measure of non-compactness techniques. The sufficient conditions of the existence and nonexistence results of nontrivial solutions for the proposed problem are investigated by introducing the Lyapunov-type inequality (LTI). Finally, our findings are compared with the existing results in the literature. The validity of the main outcomes is also tested by numerical examples with graphs and tables, and the strict minimum borders of eigenvalues for several fractional BVPs are estimated. This work is the first to deal with LTI for fractional BVP in the sense of generalized ABC derivatives.
Journal of Mathematics and Computer Science, 2026
Based on a comparison with the first-order delay equations, we obtain new criteria for oscillatio... more Based on a comparison with the first-order delay equations, we obtain new criteria for oscillation of the second-order neutral delay differential equations of the form r(t)[x(t) + q(t)x(σ(t))] ′ ′ + p(t)x(τ(t)) = 0, t ⩾ t 0 > 0. Some new results are presented that improve related ones. Our approach essentially involves establishing stronger monotonicity properties for the positive solutions of studied equations. We illustrate the improvement over the known results by applying and comparing our method with the other known results for the studied equation.
Journal of Mathematics and Computer Science, 2026
The calculus of integrals is used to solve the majority of physics and engineering issues, which ... more The calculus of integrals is used to solve the majority of physics and engineering issues, which are frequently not immediately solved. This compels us to use approximation techniques, the selection of which is based on the class of functions that meet the necessary criteria as well as known points. Within the context of quantum calculus, we present an assessment of the error of the well-known corrected dual Euler-Simpson quadrature rule in this paper. As an auxiliary result, we create a new quantum identity. Using this identity, we prove several quantum-corrected dual Euler-Simpson type integral inequalities for functions with convex q-derivatives. We allow q to go towards 1-in order to obtain the classical inequalities. We provide a few applications to wrap up this research.
Journal of Mathematics and Computer Science, 2026
This paper focuses on developing an approach for solving nonlinear Caputo-Fabrizio fractional dif... more This paper focuses on developing an approach for solving nonlinear Caputo-Fabrizio fractional differential equations (FDEs). In this approach, we use the exactness and integrating factors to solve nonlinear Caputo-Fabrizio FDE. The FDE is transformed to an ODE, and then the method of characteristics will generate an integrating factor for this ODE. Afterwards, using the exactness of differential equations concept, implicit analytical solutions of such equations are presented. We present an example to demonstrate how this approach facilitates the solution of equations that are generalized to results in previous studies.
Journal of Mathematics and Computer Science, 2026
In this study, we explore the existence of positive solutions for a class of fractional different... more In this study, we explore the existence of positive solutions for a class of fractional differential pantograph equations that incorporate the ψ-Caputo fractional derivative under specified initial conditions. By reformulating the problem as an equivalent Riemann-Liouville integral equation, we rigorously derive our principal results using the upper and lower solutions method. Lastly, we present an example to demonstrate the validity of our results.
Journal of Mathematics and Computer Science, 2026
The exponential synchronization of the coronary artery chaos system (CACS) in complex dynamical n... more The exponential synchronization of the coronary artery chaos system (CACS) in complex dynamical networks (CDNs) with state and input time-varying delays is being studied for the first time. For the CACS in CDNs, feedback control was envisioned. To enable exponential synchronization of the CACS in CDNs with continuous differential time-varying delays, an appropriate Lyapunov-Krasovskii functional (LKF) was constructed. An extended reciprocally convex matrix inequality, Jensen inequality, and Wirtinger-based integral inequality, which further decreases conservativeness, were considered when establishing the synchronization criterion. The new linear matrix inequalities (LMIs) that are required for exponential synchronization have emerged. Numerical checks may be accomplished using MATLAB's LMI toolbox. To demonstrate the efficiency of the recommended strategies, numerical examples were provided.
Journal of Mathematics and Computer Science, 2026
This study investigates the boundedness of various commutators on grand variable Herz-Hardy space... more This study investigates the boundedness of various commutators on grand variable Herz-Hardy spaces, including the Marcinkiewicz integral operator, the Calderón-Zygmund singular integral operator and the fractional integral operator. Firstly we define the Lebesgue spaces with variable exponent and some basic lemmas including Hölder's inequality for Lebesgue spaces. We use the definition of variable Herz spaces to give the definition of grand variable Herz spaces. Then we apply the atomic decomposition of grand variable Herz-Hardy spaces to obtain the boundedness of Marcinkiewicz integral operator, Calderón-Zygmund singular integral operator and fractional integral operator on grand variable Herz-Hardy spaces.
Journal of Mathematics and Computer Science, 2026
Several advanced iterative techniques for finding multiple roots of higher order, along with the ... more Several advanced iterative techniques for finding multiple roots of higher order, along with the evaluation of derivatives, have been extensively studied and documented in the literature. However, the development of higher order methods without derivatives remains a challenging task, resulting in a scarcity of such techniques in existing research. Motivated by this observation, we propose a novel eighth-order iteration function of the Traub-Steffensen type. The suggested family employs the first-order divided difference and weight functions of one and three variables, optimizing performance for multiple roots with known multiplicity. The iterative scheme requires four functional evaluations per iteration achieving optimal eighth-order convergence in the sense of the Kung-Traub conjecture with an efficiency index of 1.6818. A comprehensive convergence analysis is conducted to confirm the optimality of the proposed method. Extensive numerical testing demonstrates the stability of the theoretical predictions and the favorable convergence behavior of the new scheme. To validate its practical utility, we explore various real-world nonlinear problems involving multiple roots, such as modeling energy distribution in a blackbody radiation, root clustering, and other applications. These comparisons reveal the effectiveness of the proposed scheme relative to other eighth-order iterative methods in terms of computational order of convergence, residual error, and the difference between successive iterations. Furthermore, the stable convergence behavior of the proposed method analyzed through graphical analysis using polynomial and transcendental functions. Basins of attraction are plotted for the designed eighth-order algorithm and compared with similar methods in the field. These graphical representations highlight the superior convergence speed and overall performance of the proposed algorithm, demonstrating its robust competitiveness in solving nonlinear problems with multiple roots.
Journal of Mathematics and Computer Science, 2026
It is a familiar fact to develop inequalities using the popular method by adopting fractional ope... more It is a familiar fact to develop inequalities using the popular method by adopting fractional operators, and such study of methods is the main core of modern research in recent year. Fuzzy interval valued (FIV) mappings not only used to generalize of different convex mappings but also developed fractional operators. In this paper, we investigate fuzzy fractional inequalities for different fuzzy convexities by successfully implementing generalized fuzzy fractional operators (G-FFO). We discuss the extension of Hermite-Hadamard, trapezoid-type inequalities on the basis of fuzzy convexities and fuzzy fractional operators. Moreover, we establish the Fejér and midpoint type fuzzy inequalities for (η 1 , η 2)-convex fuzzy function.
Journal of Mathematics and Computer Science, 2026
In this paper, we give an overview of the weighted Lorentz spaces with variable exponents and als... more In this paper, we give an overview of the weighted Lorentz spaces with variable exponents and also characterize the boundedness and compactness of the composition operator on these spaces.
Journal of Mathematics and Computer Science, 2026
Integral inequalities combined with convexity in the frame of fractional calculus is an interesti... more Integral inequalities combined with convexity in the frame of fractional calculus is an interesting research topic. Mathematical inequalities and convex functions have become vital to the growth of many pure and applied fields of science. In this article, we demonstrate a few generalized fractional integral inequalities involving Raina's function that represent the Mittag-Leffler function. This article provides to an intriguing connection between convex functions, special functions, and fractional calculus. First, we present and investigate the concept of a generalized convex involving Raina's function in a polynomial context and discuss its algebraic properties. We establish the new mathematical approach of Hermite-Hadamard inequality and Pachpatte-type inequality involving the newly introduced definition via Caputo-Fabrizio fractional integral operator. Furthermore, to improve our results, we establish a new fractional lemma and utilizing this, provides some new fractional perspectives of the Hermite-Hadamard-type inequality with the aid of generalized m-convex function involving Raina's function. Applications of some of our presented results to special means are given as well. The study's conclusions provide fresh and noteworthy improvements over previous research, offering special perspectives and contributions to the area.
Journal of Mathematics and Computer Science, 2026
The purpose of this work is to improve Ferreira's results [R. A. C. Ferreira, Electron J. Differ.... more The purpose of this work is to improve Ferreira's results [R. A. C. Ferreira, Electron J. Differ. Equ., 2016 (2016), 5 pages]. The advancement is achieved through an application of Rus's contraction mapping theorem. To this end, we derive new estimates for integrals involving Green's function. Applying these estimates in conjunction with Rus's contraction mapping theorem demonstrates that a larger class of fractional boundary value problems admit a unique solution than those obtained by Ferreira. We conclude this article with numerical validation with applications, that highlight the nature and significance of the advancements made.
Journal of Mathematics and Computer Science, 2026
Linguistic interval-valued q-rung orthopair fuzzy (LIVq-ROF) sets offer a powerful framework for ... more Linguistic interval-valued q-rung orthopair fuzzy (LIVq-ROF) sets offer a powerful framework for modeling uncertainty and vagueness in complex decision-making environments. This study leverages the expressive strength of LIVq-ROF sets to develop novel aggregation operators-specifically, the LIVq-ROF Choquet integral averaging and geometric operators-which are designed to capture interdependencies among attributes in multiple attribute group decision-making (MAGDM) scenarios. The theoretical properties of these operators are rigorously established. Building on this foundation, we propose a Choquet integralbased grey relational analysis (GRA) method tailored for MAGDM under uncertainty. The proposed model is applied to a realworld case study involving the selection of the optimal neural network model for predicting crop yields. Results demonstrate the model's effectiveness in identifying the best-performing alternative. A thorough sensitivity analysis and comparison with existing approaches confirm the robustness and superior performance of the proposed method.
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Papers by Journal of Mathematics and Computer Science (JMCS)