Theory and Modern Applications
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Self-similar finite-time singularity solutions of the axisymmetric Euler equations in an infinite system with a swirl are provided. Using the Elgindi approximation of the Biot–Savart kernel for the velocity in...
We revisit our description of randomness in quantum processes that began in collaboration of Jean Ginibre. The calculations were performed on a worked example: the fluorescence of a single two-level atom pumpe...
In this paper, we tame the uncertainty about the volatility in time-averaging principle for stochastic differential equations driven by G-Brownian motion (G-SDEs) based on the Lyapunov condition. That means we...
In this paper, a model of branching processes with random control functions and affected by viral infectivity in independent and identically distributed random environments is established, and the Markov prope...
We study a multi-agent system for the modeling maritime crime. The model involves three interacting populations of ships: commercial ships, pirate ships, and coast guard ships. Commercial ships follow commerci...
The original article was published in Advances in Difference Equations 2021 2021:303
This paper investigates the existence of positive periodic solutions for a periodic predator-prey model with fear effect and general functional responses. The general functional responses can cover the Holling...
We prove that the recently introduced spin Benjamin–Ono equation admits a Lax pair and deduce a family of conservation laws that allow proving global wellposedness in all Sobolev spaces ...
Motivated by several applications, we investigate the well-posedness of a switched system composed by a system of linear hyperbolic balance laws and by a system of linear algebraic differential equations. This...
The aim of the current work is to generalize the well-known bisection method using quantum calculus approach. The results for different values of quantum parameter q are analyzed, and the rate of convergence for ...
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyse...
Although I had not previously been aware of Jean Ginibre’s work on random matrices, beginning in 1978 I became an admirer of his many papers on nonlinear waves in collaboration with Giorgio Velo. Their papers ...
The cascade of fluorescence photons by a two-level atom excited by coherent laser light is reviewed. The discussion emphasizes the random nature of resonance fluorescence and uses the distribution of delays be...
We introduce and study a variational model for signal and image analysis based on Riemann–Liouville fractional derivatives. Both the one-dimensional and two-dimensional cases are studied. The model exploits a ...
In this paper, we propose a high-order nonlinear algorithm based on a finite difference method modification to the regularized long wave equation and the Benjamin–Bona–Mahony–Burgers equation subject to the ho...
In this paper, we are concerned with the stabilization of hybrid stochastic systems with variable delay by discrete-time state feedback control. By using Lyapunov functionals, we obtain an upper bound
In this paper, we investigate the problem of pth-moment stability of stochastic functional differential equations with Markovian switching and impulsive control via comparison principle. Employing stochastic anal...
In this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional nonlinear Schrödinger equation with a cubic derivative nonlinear term containing the Hilbe...
This paper is devoted to dealing with the exponential stabilisation of highly nonlinear hybrid neutral stochastic differential equation (NSDE) by variable delay feedback control. There have been so far few res...
This paper considers a one-dimensional thermoelastic Timoshenko beam system with suspenders, general weak internal damping with time varying coefficient, and time-varying delay terms. Under suitable conditions...
The main objective of this work is two-fold. First, we investigate the stress-rate-type implicit constitutive relations for solids within the context of strain-limiting theory of material response. The relatio...
The goal of this article is to present a recently developed numerical approach for solving fractional stochastic differential equations with a singular Caputo kernel and a nonsingular Caputo–Fabrizio and Atang...
Using interpolation with biarc curves we prove Γ-convergence of discretized tangent-point energies to the continuous tangent-point energies in the
The history of the long-standing scientific collaboration between Jean Ginibre and Giorgio Velo is presented. The most important results obtained for a number of nonlinear dispersive partial differential equat...
The original article was published in Advances in Difference Equations 2020 2020:485
In this paper, by using the residue method of complex analysis, we obtain an explicit partial fraction decomposition for the general rational function
In a Hilbert setting, we study the convergence properties of the second order in time dynamical system combining viscous and Hessian-driven damping with time scaling in relation to the minimization of a nonsmo...
This paper studies a stochastic predator–prey model with Beddington–DeAngelis functional response, fear effect, and Lévy noise, where the fear is of prey induced by predator. First, we use Itô’s formula to pro...
Peridynamics is a nonlocal generalization of continuum mechanics theory which addresses discontinuous problems without using partial derivatives and replacing them by an integral operator. As a consequence, it...
It is widely accepted that financial data exhibit a long-memory property or a long-range dependence. In a continuous-time situation, the geometric fractional Brownian motion is an important model to characteri...
In this paper, we consider the stochastic optimal control problem for jump-diffusion models with state constraints. In general, the value function of such problems is the discontinuous viscosity solution of th...
We analyze the initial-boundary value problem for the mixed nonlinear Schrödinger equation posed on the half-line by using the Fokas method. Assuming that a smooth solution exists, we show that the solution ca...
The Rabinovich system can describe different physical interactions, including waves in plasmas, a convective fluid flow inside a rotating ellipsoid, and Kolmogorov’s flow interactions. This study considers the...
We prove the convergence of certain second-order numerical methods to weak solutions of the Navier–Stokes equations satisfying, in addition, the local energy inequality, and therefore suitable in the sense of ...
Nonorthogonal polynomials have many useful properties like being used as a basis for spectral methods, being generated in an easy way, having exponential rates of convergence, having fewer terms and reducing c...
This paper investigates the quasiconsensus problem of fractional-order heterogeneous multiagent systems, the distributed impulsive control protocol is designed for the multiagent system. In contrast to some ex...
This paper investigates a globally coupled map lattice. Rigorous proofs to the existence of chaos in the sense of both Li–Yorke and Devaney in two controlled globally coupled map lattices are presented. In add...
In this paper, we replace the standard numerical approach of estimating parameters in a mathematical model using numerical solvers for differential equations with a physics-informed neural network (PINN). This...
Peridynamic (PD) theories have become widespread in various research areas due to the ability of modeling discontinuity formation and evolution in materials. Bond-based peridynamics (BB-PD), notwithstanding so...
Parametric interpolatory curves play a vital part in geometric modeling. Cubic Catmull–Rom spline is a well-known tool for constructing parametric interpolatory curves, but it cannot be modified once its contr...
We devise a numerical scheme for computing arc-length parameterized curves of low bending energy that are confined to convex domains. We address the convergence of the discrete formulations to a continuous mod...
In this work, the Chebyshev collocation scheme is extended for the Volterra integro-differential equations of pantograph type. First, we construct the operational matrices of pantograph and derivative based on...
Image denoising approaches based on partial differential modeling have attracted a lot of attention in image processing due to their high performance. The nonlinear anisotropic diffusion equations, specially P...
In this study, the time-dependent potential coefficient in a higher-order PDE with initial and boundary conditions is numerically constructed for the first time from a nonlocal integral condition. Even though ...
In this paper, we focus on the development and study of the finite difference/pseudo-spectral method to obtain an approximate solution for the time-fractional diffusion-wave equation in a reproducing kernel Hi...
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08 May 2020
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