Theory and Modern Applications
Page 2 of 98
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...
In this paper, we construct a new linear second-order finite difference scheme with two parameters for space-fractional Allen–Cahn equations. We first prove that the discrete maximum principle holds under reas...
The goal of this paper is to present a new class of operators satisfying the Prešić-type rational η-contraction condition in the setting of usual metric spaces. New fixed point results are also obtained for these...
In this paper, we establish an SIVR model with diffusion, spatially heterogeneous, latent infection, and incomplete immunity in the Neumann boundary condition. Firstly, the threshold dynamic behavior of the mo...
We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover nonlinear variational problems such as the p-Laplace equation or the Modica–Mortola energy with esse...
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 deriva...
This paper is concerned with the Cauchy problem for semilinear wave equation with space-dependent scattering damping and combined nonlinearities. The blowup results of solution are established by introducing p...
The aim of the manuscript is to present the concept of a graphical double controlled metric-like space (for short, GDCML-space). The structure of an open ball of the proposed space is also discussed, and the n...
In this paper, we present a numerical method to solve ordinary differential equations (ODEs) by using neural network techniques in a deferred correction method framework. Similar to the deferred or error corre...
We examine a class of nonlinear fractional Mathieu equations with a damping term. The equation is an important equation of mathematical physics as it has many applications in various fields of the physical sci...
In this manuscript, we examine both the existence and the stability of solutions to the boundary value problem of Caputo fractional differential equations of variable order by converting it into an equivalent ...
The uncertain production-inventory problem with deteriorating items is investigated and an optimal control model is developed in the present paper. The uncertain production-inventory problem is perturbed by an...
In this work, we study the dynamical behavior of a modified SIR epidemiological model by introducing negative feedback and a nonpharmaceutical intervention. The first model to be defined is the Susceptible–Iso...
In this study, the event-triggered finite-time consensus problem of a class of general linear leader-follower multi-agent systems with unmeasurable states is investigated. First, an observer-based distributed ...
In this paper, we study the problem for pricing of American better-of option on two assets. Due to two correlated underlying assets and early-exercise feature which requires two free boundaries to be determine...
This paper is concerned with the well-posedness problem of a doubly degenerate parabolic equation with variable exponents. By the parabolically regularized method, the existence of local solution is proved. Mo...
In this article, we present a fractional Kersten–Krasil’shchik coupled KdV-mKdV nonlinear model associated with newly introduced Atangana–Baleanu derivative of fractional order which uses Mittag-Leffler functi...
In this paper, we investigate periodic boundary value problems for Caputo type fractional semilinear nonautonomous differential equations with non-instantaneous impulses. By using semigroup theory combined wit...
In order to describe the dynamic process of epidemic transmission with vertical transmission and vaccination in more detail and to better track the factors that lead to the occurrence of epidemics, we construc...
We investigate the fractional dynamics of a coronavirus mathematical model under a Caputo derivative. The Laplace–Adomian decomposition and Homotopy perturbation techniques are applied to attain the approximat...
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 difference equations are studied deeply and extensively by many scientists by using fixed-point theorems on different types of function spaces. In this study, we combine fixed-point theory...
Study of ecosystems has always been an interesting topic in the view of real-world dynamics. In this paper, we propose a fractional-order nonlinear mathematical model to describe the prelude of deteriorating q...
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 var...
This research paper designs the noninteger order SEITR dynamical model in the Caputo sense for tuberculosis. The authors of the article have classified the infection compartment into four different compartment...
Fractional differential equations have recently demonstrated their importance in a variety of fields, including medicine, applied sciences, and engineering. The main objective of this study is to propose an Ad...
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 function...
In this paper, we are concerned with the oscillation of solutions to a class of fourth-order delay differential equations with p-Laplacian like operators
In this paper, we establish some new inequalities of Simpson’s type for differentiable convex functions involving some parameters and generalized fractional integrals. The results given in this study are a gen...
This work is concerned with the issue of dissipative filtering for stochastic semi-Markovian jump via neural networks where the time-varying delay is based upon another semi-Markov process. Dissipative perform...
2022 Citation Impact
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2.9 - 5-year Impact Factor
1.702 - SNIP (Source Normalized Impact per Paper)
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04 September 2019