Journal of Applied Mathematics and Computing最新文献

The resolvability parameter is an essential component, especially in the context of network research, due to its theoretical and practical significance. Its importance is evident in several applications and outcomes, including social network analysis, network security, facility location and site selection, and effective routing. We introduce a novel resolvability parameter, Fault-Tolerant Mixed Metric Dimension, in this paper, and this defined as let (R_{m,f}) be a set that nodes on a graph as both an edge-resolving set and a resolving set. If (R_{m,f}) can uniquely represent the graph’s edges and vertices, then it is referred to as a mixed resolving set, and its all subsets cardinality is called the mixed metric dimension. If all of the graph’s vertices and edges are uniquely represented by (R_{m,f}^{prime },) and all subsets of (R_{m,f}^{prime }) with of cardinality one less than (R_{m,f}) likewise have unique representations for all of the graph’s vertices and edges, then (R_{m,f}) is referred to as a Fault-Tolerant Mixed Resolving Set, and If two such sets (R_{m,f}^{1}) and (R_{m,f}^{2}) exist such that (R_{m,f}^{1}cap R_{m,f}^{2}ne 0) then we say that the graph has exchange property. (R_{m,f})’s minimum cardinality is known as its fault-tolerant mixed Metric Dimension. These definitions offer a means of measuring a collection of vertices’ capacity to represent graph structures uniquely, taking fault-tolerant and resolution into account. Furthermore, a problem related to the lab’s system network is also discussed and linked with this topic in this work. Like a lab engineer is embarking on the creation of a new circular lab, intending to establish where and how many devices within it to supply internet with wire to all systems. A solution to this problem is proving this novel topic authenticity.

The article studies fixed/preassigned-time synchronization in a fuzzy inertial neural network characterized by discontinuous activation functions and mixed delays. First, we adopt a more accurate method to calculate the settling-time. Then, we extend the result of fixed-time synchronization (FXS) to preassigned-time synchronization (PAS). Next, by designing event-triggered controller and applying the non-smooth theory, the stability criterion of FXS/PAS are obtained. Finally, in the simulation section, we illustrate the validity and practicability of the results by listing a specific example.

In the context of hyperbolic spaces, our study presents a novel iterative approach for approximating common fixed points satisfying general contractive condition involving a pair of mappings with weak compatibility. Also, we notice that our iterative procedure approximates to a point of coincidence if the weak compatibility condition is violated. We provide theorems to demonstrate the (Delta -)convergence, stability, and efficiency of this iteration process. Additionally, we provided some immediate corollaries that involve mappings with contractive condition, instead of general contractive condition. Furthermore, we demonstrate with examples and graphs that our iteration process is faster than all previous procedures, including those of Jungck-SP, Jungck-CR, and Jungck-DK, utilizing MATLAB software. Also, we compare the impact of the initial values and the parameters on the convergence behavior of the proposed iterative process with existing iterative schemes using an example. Finally, we focus on using our iterative technique to approximate the solution of a non-linear integral equation with two delays.

This paper exploits the good features of the Dai-Liao (DL) conjugate gradient (CG) method in connection with the inertial interpolation and the projection technique to propose an efficient algorithm for solving the convex-constrained monotone system by avoiding the direction of maximum magnification (MM). It is well-known that if the gradient lies in the direction of MM by the search direction matrix, the algorithm may result in unnecessary computational errors and may likely not be convergent. Avoiding this direction will accelerate the convergence of the proposed algorithm theoretically and numerically. The proposed DL algorithm avoids the direction of MM and uses the inertial extrapolation and hyperplane projection steps to accelerate its convergence at every given iteration. The theoretical analysis proved that the proposed algorithm is globally convergent under some standard assumptions and has a linear convergence rate. Lastly, the numerical experiment on some test problems demonstrated that the algorithm is time-efficient and has less computational cost.

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.