Journal of Applied Mathematics and Computing最新文献

This paper presents novel fixed-point results for two distinct families of fuzzy-dominated operators satisfying a generalized nonlinear contraction condition on a closed ball in a complete strong b-metric-like space. Our research introduces innovative fixed-point theorems for separate families of ordered fuzzy-dominated mappings in ordered complete strong b-metric-like spaces. Two different kinds of mappings are used in our methodology: a class of fuzzy-dominated mappings and a class of strictly non-decreasing mappings. Furthermore, we establish new fixed-point results for fuzzy-graph-dominated contractions. To substantiate our findings, we provide both rigorous and illustrative examples. We demonstrate the uniqueness of our results by applying them to obtain common solutions for fractional differential equations and fuzzy Volterra integral equations.

The aim of the present paper is to suggest a novel technique based on the operational matrix approach for solving a fractional weakly singular two-dimensional partial Volterra integral equation (FWS2DPVIE) using numerical methods. In this technique, Boubaker polynomials are used to create operational matrices. The technique consists of two major phases. In the first step, Boubaker polynomials are employed to generate operational matrices, which help in transforming the problems into systems of algebraic equations. In the second step, the algebraic equations are numerically solved.The suggested technique is also compared with existing approaches. The results show that the suggested technique outperforms its counterparts, demonstrating its superiority.

Calcium is a decisive messenger for neuronal vivid functions. The calcium intracellular sequestering major unit is the Endoplasmic Reticulum (ER). Brownian motion of calcium could be bound to different buffers like S100B, calmodulin, etc, and different organelles. Plasma membrane channels like voltage-gated calcium channels (VGCC) and Plasma Membrane Calcium ATPase (PMCA), Orai channel could perturb the calcium concentration. To investigate the calcium interplay for intracellular signaling we have developed the two-dimensional time fractional reaction–diffusion equation. To solve this model analytically, we have used the Laplace and Fourier cosine integral transform method. By using Green’s function we obtained the compact solution in closed form with Mainardi’s function and Wright’s function. Uniqueness and existence proved the more fundamental approach to the fractional reaction–diffusion problem. The fractional Caputo approach gives better insight into this real-life problem by its nonlocal nature. Significant effects of different parameters on free calcium ions were obtained and the results are interpreted with normal and Alzheimeric cells. Non-local property and dynamical aspects are graphically presented which might provide insight into the Stromal interaction molecule (STIM) and S100B parameters.

Consider the reality that flocking behavior is affected by random noise. We study the Cucker–Smale-type systems with multiplicative noise where the communication weight satisfies the long-range fat tail condition. By comparing with the related deterministic system, we show that the noise intensity of the stochastic system mainly affects the convergence speed of the flocking. Specifically, we demonstrate that the system can achieve a stochastic finite-time flocking when the noise intensity is small, and almost surely asymptotic flocking when the noise intensity is large. Some numerical simulations are given to show our theoretical results. In addition, the method in this work can improve the results of previous studies.

The fractional ordered mathematical model offers more insights compared to integer order models. In this work, we analyzed fractional order rat bite fever model. We employ the Adams–Bashforth–Moulton method in conjunction with fractional-order derivatives in the Caputo sense to study the model. The work demonstrates how fractional derivative models offer an increased degree of flexibility to investigate memory effects and illness dynamics for a particular data set. Further, an analysis of the aforementioned model including its existence, uniqueness, and stability is considered. The distinct parameter estimation for every value of the fractional order highlights the importance of this work.

Hepatitis is inflammation of the liver, and one of its types, hepatitis B, is a contagious infection. Using mathematical models, the nature of the spread of the Hepatitis B virus can be predicted. In the present paper, a hepatitis B epidemic model with a Beddington–DeAngelis type incidence rate and a constant vaccination rate is considered. Some dynamical properties of this model, such as non-negativity, boundedness character, the basic reproduction number (mathcal {R}_0), stability nature, and the bifurcation phenomenon, are investigated. By the Bendixson theorem, it is demonstrated that the disease-free equilibrium is globally asymptotically stable. It is shown that a transcritical bifurcation phenomenon occurs when (mathcal {R}_0=1). It is concluded that the endemic equilibrium is globally asymptotically stable when (mathcal {R}_0>1), by utilizing Dulac’s criteria. Also, a discrete system of difference equations is obtained by constructing a non-standard finite difference (NSFD) scheme for the continuous model. It is shown that the solutions of this discrete system are dynamically consistent for all finite step sizes. The theoretical results obtained are also supported and visualized by numerical simulations. These simulations also demonstrate that the NSFD scheme produces much more efficient results than the Euler or RK4 schemes, as shown in the theoretical results obtained.

Eigenvalue decomposition of quaternion Hermitian matrices is a crucial mathematical tool for color image reconstruction and recognition. Quaternion Jacobi method is one of the classical methods to compute the eigenvalues of a quaternion Hermitian matrix. Using quaternion Jacobi rotations, this paper brings forward an innovative method for the eigenvalue decomposition of dual quaternion Hermitian matrices. The effectiveness of the proposed method is confirmed through numerical experiments. Furthermore, a dual complex matrix representation for the color image is developed, and the dual quaternion Jacobi method is applied to the eigenvalue problems of dual complex Hermitian matrices. This approach achieves successful results in the color images reconstruction and recognition. Compared to the quaternion matrix representation of the color image, this approach makes computations more convenient when dealing with problems related to color image processing.

Fermentation is an indispensable link in wine brewing, and mathematical modeling is an effective means to study fermentation process, which can reveal the characteristics of state variables and help to optimize the control of fermentation process. In this paper, a new model with fractional derivative of the wine fermentation is proposed. The basic properties of the solution and the stability at the equilibrium point of the new model are proved. Then the numerical simulation of the fractional wine fermentation model is given by the generalized Euler method. Compared with the classical integer order wine fermentation model, the new fractional wine fermentation model proposed in the article is more responsive and reflects more comprehensive trends through qualitative and quantitative analysis. We expect that this fractional wine fermentation model can be applied to wine production in real world, which is beneficial for oenologists to grasp all kinds of data more accurately, thus improving the quality of wine.

In the present article, we introduce a Durrmeyer variant of certain approximation operators. We estimate the moment-generating function and moments of these operators employing the Lambert W function and establish some direct results. We further provide a composition of these operators with Szász–Mirakjan operators and estimate direct results for the composition operator. Additionally, we provide a graphical comparison of the approximation properties of the operators.

This study investigates breast cancer dynamics using modified ABC-fractional operators. We examine interactions among cancer stem cells, tumor cells, healthy cells, excess estrogen effects, and immune cells. By applying the “Localization of Compact Invariant Sets” technique and comparison theory, we establish conditions for cancer persistence without immune cells and eradication with an immune response. We analyze equilibria, global attraction persistence state, stability, solution uniqueness, and existence using recursive sequences and fixed point theorem. Numerical simulations with Lagrange’s interpolation validate and deepen our understanding of breast cancer dynamics. Incorporating modified ABC-fractional derivatives enhances our comprehension of the model.