Stability of Fuzzy Dynamical Systems via Lyapunov FunctionsRead the full article
International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.
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On One Evolution Equation of Parabolic Type with Fractional Differentiation Operator in Spaces
In the paper, we investigate a nonlocal multipoint by a time problem for the evolution equation with the operator , , and is a fixed parameter. The operator is treated as a pseudodifferential operator in a certain space of type . The solvability of this problem is proved. The representation of the solution is given in the form of a convolution of the fundamental solution with the initial function which is an element of the space of generalized functions of ultradistribution type. The properties of the fundamental solution are investigated. The behavior of the solution at (solution stabilization) in the spaces of generalized functions of type and the uniform stabilization of the solution to zero on are studied.
Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D
This paper shows the existence, uniqueness, and asymptotic behavior in time of regular solutions (a la Ladyzhenskaya) to the Bénard problem for a heat-conducting fluid model generalizing the classical Oberbeck–Boussinesq one. The novelty of this model, introduced by Corli and Passerini, 2019, and Passerini and Ruggeri, 2014, consists in allowing the density of the fluid to also depend on the pressure field, which, as shown by Passerini and Ruggeri, 2014, is a necessary request from a thermodynamic viewpoint when dealing with convective problems. This property adds to the problem a rather interesting mathematical challenge that is not encountered in the classical model, thus requiring a new approach for its resolution.
Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model
The aim of the present study is to analyze and find a solution for the model of nonlinear ordinary differential equations (ODEs) describing the so-called coronavirus (COVID-19), a deadly and most parlous virus. The mathematical model based on four nonlinear ODEs is presented, and the corresponding numerical results are studied by applying the variational iteration method (VIM) and differential transformation method (DTM).
Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation
We study the global existence and asymptotic behavior of the solutions for two-fluid compressible isentropic Euler–Maxwell equations by the Fourier transform and energy method. We discuss the case when the pressure for two fluids is not identical, and we also add friction between the two fluids. In addition, we discuss the rates of decay of norms for a linear system. Moreover, we use the result for estimates to prove the decay rates for the nonlinear systems.
Solvability in Gevrey Classes of Some Nonlinear Fractional Functional Differential Equations
Our purpose in this paper is to prove, under some regularity conditions on the data, the solvability in a Gevrey class of bound −1 on the interval of a class of nonlinear fractional functional differential equations.
Stability Analysis of a Fractional-Order Model for Abstinence Behavior of Registration on the Electoral Lists
In this work, we propose a fractional-order model that describes the dynamics of citizens who have the right to register on the electoral lists and the negative influence of abstainers on the potential electors. By using Routh–Hurwitz criteria and constructing Lyapunov functions, the local and the global stability of abstaining-free equilibrium and abstaining equilibrium are obtained. Finally, some numerical simulations are performed to verify the theoretical analysis, and they are given for different parameter setting of the order of derivative .