Advances in Continuous and Discrete Models
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Random exponential attractor for a stochastic reaction-diffusion equation in $L^{2p}(D)$
Advances in Continuous and Discrete Models - Tập 2024 Số 1 - Trang 1-24 - 2024
In this paper, we establish some sufficient conditions for the existence of a random exponential attractor for a random dynamical system in a Banach space. As an application, we consider a stochastic reaction-diffusion equation with multiplicative noise. We show that the random dynamical system $\phi(t,\omega)$ generated by this stochastic reaction-diffusion equation is uniformly Fréchet different......
Switched hyperbolic balance laws and differential algebraic equations
Advances in Continuous and Discrete Models - Tập 2023 - Trang 1-31 - 2023
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 setting includes networks and looped systems of hyperbolic balance laws. The obtained results are globally in time, provided that the inputs have finite (but not necessarily small) total var......
On some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications
Advances in Continuous and Discrete Models - Tập 2022 - Trang 1-18 - 2022
In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of o......
Analytical analysis of fractional-order sequential hybrid system with numerical application
Advances in Continuous and Discrete Models - Tập 2022 - Trang 1-19 - 2022
We investigate a general sequential hybrid class of fractional differential equations in the Caputo and Atangana–Baleanu fractional senses of derivatives. We consider the existence and uniqueness of solutions and the Hyers–Ulam (H-U) stability for a general class. We use the Banach and Leray–Schauder alternative theorems for the existence criteria. With the help of nonnegative Green’s functions, t......
Complete controllability of nonlinear fractional neutral functional differential equations
Advances in Continuous and Discrete Models - Tập 2022 - Trang 1-11 - 2022
This paper is concerned with the complete controllability of a nonlinear fractional neutral functional differential equation. Some sufficient conditions are established for the complete controllability of the nonlinear fractional system. The conditions are established based on the fractional power of operators and the fixed-point theorem under the assumption that the associated linear system is co......
Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocksAbstract This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in... ...
Advances in Continuous and Discrete Models - Tập 2022 Số 1
Analysis of a stochastic predator–prey system with fear effect and Lévy noise
Advances in Continuous and Discrete Models - Tập 2022 - Trang 1-24 - 2022
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 prove the existence and uniqueness of a global positive solution and its moment boundedness. Next, sufficient conditions for the persistence and extinction of both species are given. We further ......
Operator compression with deep neural networks
Advances in Continuous and Discrete Models - Tập 2022 - Trang 1-23 - 2022
This paper studies the compression of partial differential operators using neural networks. We consider a family of operators, parameterized by a potentially high-dimensional space of coefficients that may vary on a large range of scales. Based on the existing methods that compress such a multiscale operator to a finite-dimensional sparse surrogate model on a given target scale, we propose to dire......
On the maximum principle for relaxed control problems of nonlinear stochastic systemsAbstract We consider optimal control problems for a system governed by a stochastic differential equation driven by a d-dimensional Brownian motion where both the drift and the diffusion coefficient are controlled. It is well known that without additional convexity conditions the strict control problem does not admit an optimal control. To overcome this difficulty, ... ...
Advances in Continuous and Discrete Models -
Retraction Note: Hermite–Hadamard-type inequalities for $\eta _{h}$ -convex functions via ψ-Riemann–Liouville fractional integrals
Advances in Continuous and Discrete Models - Tập 2022 - Trang 1-1 - 2022
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