Mathematical Methods in the Applied Sciences最新文献

This paper investigates the local exponential synchronization-like control between state-dependent impulsive chaotic neural networks. First, various adequate conditions are theoretically proven to guarantee that the trajectory of every solution for the chaotic neural networks passes through each impulsive surface only once. Second, by designing segmented controllers and aperiodic intermittent controllers, respectively, making use of the comparison principle and linear matrix inequality techniques, this paper establishes adequate conditions for the local exponential synchronization-like control between impulsive chaotic neural networks. Finally, the validity of the proposed results was confirmed by using examples and numerical simulations.

In this paper, we introduce and study a new class of split inverse problems called bilevel split hierarchical variational inequality problem with multiple output sets in the framework of real Hilbert spaces. We propose a viscosity-type Tseng's extragradient method for solving this problem when the cost operators are pseudomonotone. Under mild conditions, we obtain a strong convergence result for the proposed algorithm. Finally, we present numerical experiments to illustrate the applicability of our method.

We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and the coagulation-fragmentation system with binary fragmentation. Under reasonable general condition on the rate coefficients we establish the existence of admissible solutions, meaning solutions that are obtained as appropriate limit of solutions to a finite-dimensional truncation of the infinite-dimensional ODE. For these solutions, we prove that, in the class of models, we call isolated both the total number of particles and the total mass are conserved, whereas in those models, we can non-isolated only the mass is conserved. Additionally, under more restrictive growth conditions for the rate equations, we obtain uniqueness of solutions to the initial value problems.

The focus of this paper is to present a new fourth-order local meshfree technique for numerically solving the multiterm time-fractional partial integro-differential equation. The time-fractional derivative term, defined in the Caputo sense, is approximated using the weighted and shifted Grünwald difference (WSGD) formula. Also, a second-order technique for approximating the integral term in the Riemann–Liouville sense leads to the semidiscrete formulation of the model. Applying the meshless radial basis function (RBF)-Hermite finite difference (RBF-HFD) technique for spatial discretization completes the model's discretization process. The novelty of this method lies in the approximation of the Laplace operator using the Hermite RBF interpolation over local stencils. This leads to RBF-generated Hermite finite difference (RBF-HFD) formula, which provides a significant improvement in the accuracy and computational efficiency. Its meshfree nature also makes it very suitable for solving partial integro-differential equations (PIDEs) on irregular domains. In the subsequent discussion, the unconditional stability and convergence of the time-discrete scheme are proven via the energy method.The accuracy and efficiency of the proposed scheme are investigated through numerical simulations on regular and irregular domains. Furthermore, the numerical outcomes are compared with existing methods in the literature to highlight the accuracy and efficiency of the present technique.

There are dozens of languages spoken worldwide, but due to linguistic shifts and rivalry, many of them are in danger of becoming extinct. A vital component, therefore, is linguistic sustainability because cultural sustainability depends on language preservation. To represent linguistic sustainability, which traditional models do not adequately present, this work presents a novel fractional-order method that uses both constant and variable fractional-order derivatives. The significance of the arbitrary order derivative and the theoretical conclusions we got were validated by implementing a recently suggested Toufik–Atangana numerical technique with Caputo (C), Caputo–Fabrizio (CF), and Atangana Balaneau Caputo (ABC) fractional derivatives. Additionally, a comparison between the Mathematica NDSolve approach and the integer order Toufik-Atangana method was done. This innovative method provides insightful information for language preservation plans, allowing linguists and policymakers to create more potent interventions to save endangered languages.

In this study, we deal with the perturbed nonlinear Schrödinger equation (PNLSE). This equation is an important model for describing optical soliton propagation in nonlinear optical fibers with the Kerr law nonlinearity. Two efficient techniques are employed: the generalized Abel equation method (GAEM) with variable coefficients and the collective variable (CV) approach. As a consequence of GAEM, we derive a periodic-type soliton solution and enhance its physical interpretation through graphical simulations. The CV method, carrying a fourth-order Runge–Kutta scheme and the Gaussian ansatz, is used to model the dynamics of soliton parameters such as amplitude, width, chirp, and frequency, revealing periodic fluctuations influenced by propagation distance. Both methods provide a comprehensive understanding of soliton behaviors in optical fibers, offering valuable outcomes for advancing optical communication systems.