Differential Inclusions Research Articles

(Non-state) actors in internal bordering and differential inclusion: Syrian refugees’ housing experience in Turkey

ABSTRACT Turkey, as the largest refugee-hosting country, provides insights into the externalization of European borders and the internalization of its own borders. Oscillating between open-door and strict-border policies, alongside the political inactiveness of public authorities and CSOs governing Syrian mobility, Turkey reveals crucial dynamics. Focusing on Syrian refugees’ housing in a refugee hub of Izmir, this study unravels internal bordering and explores its rationales and the involvement of non-state actors. Syrian refugees encounter three internal bordering mechanisms affecting their housing inclusion: selective overpricing, ethnic filtering and arbitrary interrogations. These differential inclusion practices, led by market actors (landlords and realtors), ethnic networks, and street-level bureaucrats (mukhtars and municipal officers), are driven by the prevalence of anti-refugee sentiment in Turkey, where Syrians are perceived as unwanted or undeserving. The internal bordering mechanisms are rooted in ethnic, economic, cultural, and security-based rationales, influenced by the personal interests and socio-economic backgrounds of the involved actors.

Finite-time synchronization of proportional delay memristive competitive neural networks

The finite-time synchronization (FTS) is considered for proportional delay memristive competitive neural networks (PDMCNNs). By utilizing Lyapunov functional method and differential inclusion theory, two new criteria ensuring the FTS of PDMCNNs are established. These criteria with algebraic inequality forms are less complicated and easier to verify than the matrix inequality forms. In addition, the corresponding settling times have been estimated. Eventually, the effectiveness of the presented criteria and controllers is confirmed through two numerical examples, and one application about image encryption is provided.

Non-fragile output-feedback control for delayed memristive bidirectional associative memory neural networks against actuator failure

This article investigates the stabilization property for the modeled memristive bidirectional associative memory neural networks with time-varying delay when the faulty signals received from the fluctuated controller. The non-fragile output-feedback controller is taken into account to counteract the impact of gain perturbations to end up with robust fault-tolerant setup. To tackle the weak signals in the actuator received from the fluctuated controller, control gain matrices encompass situations intended to memory non-fragile output-feedback controller. Based on the Lyapunov stability theory, differential inclusion theory, and congruence transformation, the sufficient condition for the global asymptotic stabilization property for the designed fault-tolerant memristive bidirectional associative memory neural network model is obtained in terms of linear matrix inequality by utilizing Wirtinger's inequality. Finally, numerical examples are approached with the state performance plots of the proposed memristive bidirectional associative memory neural network model with respect to the time-domain plane, to confirm the stabilization results and it illustrates the working mechanism of the designed controller.

Approximate Controllability of Hilfer Fractional Stochastic Evolution Inclusions of Order 1 < q < 2

This paper addresses the approximate controllability results for Hilfer fractional stochastic differential inclusions of order 1<q<2. Stochastic analysis, cosine families, fixed point theory, and fractional calculus provide the foundation of the main results. First, we explored the prospects of finding mild solutions for the Hilfer fractional stochastic differential equation. Subsequently, we determined that the specified system is approximately controllable. Finally, an example displays the theoretical application of the results.

Fixed-time synchronization of interconnected memristive neural networks with energy consumption via switched control

The fixed-time synchronization of time-delay interconnected memristive neural networks is probed in this article. Firstly, according to the conventional controller, a new type of switching controller is proposed, which can complement each other. By utilizing the theory of Lyapunov stability and differential inclusion, it is proved that interconnected memristive neural networks can achieve synchronization within a fixed time under the designed controller. In addition, to control engineering costs, the upper limit of energy consumption, which is produced by the controller from the initial time to the settling-time, is estimated. Finally, numerical examples are provided to verify the validity of the theoretical results.

Finite-time stability of fractional-order quaternion-valued memristive neural networks with time delay

This study addresses the finite-time stability (FTS) problem of fractional-order quaternion-valued memristive neural networks (FQMNNs) with time delay. Firstly, by leveraging set-valued mapping, differential inclusion, and contracting mapping principle, the sufficient condition is provided to assure the existence and uniqueness of the equilibrium point. Secondly, given the fractional order differential inequality and Gronwall inequality, a finite-time stability (FTS) criterion is obtained for the delayed FQMNNs with the fractional order between 0 and 1. Additionally, a sufficient condition is proposed to guarantee the FTS of FQMNNs with the fractional order between 1 and 2. Compared with existing results, this study not only extends the fractional order between 0 and 2, but also incorporates quaternions, which significantly enhances the FTS theory. Finally, two numerical examples demonstrate the practicality of the obtained results.

Some Existence Results of Coupled Hilfer Fractional Differential System and Differential Inclusion on the Circular Graph

Some Existence Results of Coupled Hilfer Fractional Differential System and Differential Inclusion on the Circular Graph

Existence and Stability of Solutions for p-Proportional ω-Weighted κ-Hilfer Fractional Differential Inclusions in the Presence of Non-Instantaneous Impulses in Banach Spaces

In this work, we introduce a new definition for the fractional differential operator that generalizes several well-known fractional differential operators. In fact, we introduce the notion of the p-proportional ω-weighted κ-Hilfer derivative includes an exponential function, Da,λσ,ρ,p,κ,ω, and then we consider a non-instantaneous impulse differential inclusion containing Da,λσ,ρ,p,κ,ω with order σ∈(1,2) and of kind ρ∈[0,1] in Banach spaces. We deduce the relevant relationship between any solution to the studied problem and the integral equation that corresponds to it, and then, by using an appropriate fixed-point theorem for multi-valued functions, we give two results for the existence of these solutions. In the first result, we show the compactness of the solution set. Next, we introduce the concept of the (p,ω,κ)-generalized Ulam-Hyeres stability of solutions, and, using the properties of the multi-valued weakly Picard operator, we present a result regarding the (p,ω,κ)-generalized Ulam-Rassias stability of the objective problem. Since many fractional differential operators are particular cases of the operator Da,λσ,ρ,p,κ,ω, our work generalizes a number of recent findings. In addition, there are no past works on this kind of fractional differential inclusion, so this work is original and enjoyable. In the last section, we present examples to support our findings.

Zero-error tracking control of quantized iterative learning for differential inclusion systems with channel fading

Zero-error tracking control of quantized iterative learning for differential inclusion systems with channel fading

The local representation of incrementally scattering passive nonlinear systems

AbstractWe investigate the local (in time) description of incrementally scattering passive nonlinear systems. We show that these systems can be defined by a differential inclusion and a function that gives the current output in term of the current state and the current input. Our approach uses the theory of maximal monotone operators and Lax–Phillips-type nonlinear semigroups.

Integrable Solutions and Continuous Dependence of a Nonlinear Singular Integral Inclusion of Fractional Orders and Applications

Let E be a reflexive Banach space. In this article we study the existence of integrable solutions in the space of all lesbesgue integrable functions on E, L1([0,T],E), of the nonlinear singular integral inclusion of fractional orders beneath the assumption that the multi-valued function G has Lipschitz selection in E. The main tool applied in this work is the Banach contraction fixed point theorem. Moreover, the paper explores a qualitative property associated with these solutions for the given problem such as the continuous dependence of the solutions on the set of selections S1G(τ,x(τ)). As an application, the existence of integrable solutions of the two nonlocal and weighted problems of the fractional differential inclusion is investigated. We additionally provide an example given as a numerical application to demonstrate the effectiveness and value of our results.

Fractional-order differential inclusion with pseudo-Lipschitz multi-valued map

In this paper, we investigate the existence of a solution for a fractional-order differential inclusion when the multi-valued map is supposed to be non-convex and satisfies a pseudo-Lipschitz property. For our aim, we use Filippov's theorem. An application to an optimal control problem is also presented for a fractional differential equation.

Existence of Solutions for Caputo Sequential Fractional Differential Inclusions with Nonlocal Generalized Riemann–Liouville Boundary Conditions

Existence of Solutions for Caputo Sequential Fractional Differential Inclusions with Nonlocal Generalized Riemann–Liouville Boundary Conditions

On the Formation of Microstructure for Singularly Perturbed Problems with Two, Three, or Four Preferred Gradients

In this manuscript, singularly perturbed energies with 2, 3, or 4 preferred gradients subject to incompatible Dirichlet boundary conditions are studied. This extends results on models for martensitic microstructures in shape memory alloys (N=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=2$$\\end{document}), a continuum approximation for the J1-J3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_1-J_3$$\\end{document}-model for discrete spin systems (N=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=4$$\\end{document}), and models for crystalline surfaces with N different facets (general N). On a unit square, scaling laws are proved with respect to two parameters, one measuring the transition cost between different preferred gradients and the other measuring the incompatibility of the set of preferred gradients and the boundary conditions. By a change of coordinates, the latter can also be understood as an incompatibility of a variable domain with a fixed set of preferred gradients. Moreover, it is shown how simple building blocks and covering arguments lead to upper bounds on the energy and solutions to the differential inclusion problem on general Lipschitz domains.

Existence of solution of a system of non-linear differential inclusions with non-local, integral boundary conditions via fixed points of hybrid contractions

In the present article, we have introduced the notions of γ-admissibility for the pair of q-ROF set-valued maps and admissible hybrid q-ROF Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{Z}$\\end{document}-contraction. Notions introduced in the article generalizes the existing concepts in fuzzy literature. Common fixed point result for a pair of γ-admissible q-ROF mappings in b-metric spaces utilizing the introduced contraction is presented. A nontrivial example to support the obtained results is also included. As an application, we have discussed the existence of solution of system of non-linear n-th order differential inclusions with non-local and integral boundary conditions.

Nonsmooth Integral Guiding Potentials in the Problem of the Asymptotic Behavior of Trajectories of Some Classes of Functional Differential Inclusions

Nonsmooth Integral Guiding Potentials in the Problem of the Asymptotic Behavior of Trajectories of Some Classes of Functional Differential Inclusions

Fixed-time control and estimation of discontinuous fuzzy leakage-delayed networks: Indefinite and economical conditions of Filippov systems

This paper considers the fixed-time stability of Filippov systems and discontinuous networks described by the Filippov systems. Firstly, the more generalized and economical inequality condition on Lyapunov function is proposed, which can not only improve the previous negative definite conditions, but also the indefinite conditions. Based on the definition of the Lyapunov stability and finite-time convergence, new fixed-time stability lemmas are proposed and the settling-time is also estimated. In order to apply the new fixed-time stability lemmas to the neural networks, fixed-time stabilization of a class of fuzzy leakage-delayed neural networks with discontinuous activations is considered which is rarely studied since the delay is leakage and activations are discontinuous and they are not easy to deal with simultaneously. By means of the Filippov regularization and differential inclusions theory, new criteria on the stabilization of the considered networks are derived via the new modified non-chattering controller, which can improve the previous ones with parameter and symbolic function. Finally, example and numerical simulations further examine the correctness of the main results.

Approximation of the HJB viscosity solutions in differential inclusion optimal control with state constraint

This paper tries to investigate a differential inclusion optimal control problem with state constraint (P) through an approximation of Hamilton–Jacobi–Bellman viscosity solutions. By invoking a duality result between the control problem (P) and the upper hull of viscosity subsolutions of the HJB equation, we prove that value functions of the discrete problems are solutions of discrete Bellman equations and converge to the value function of (P). We also establish that the optimal trajectory sequence of discrete problems converges to the solution of the optimal control problem (P). The idea behind the approximation is based on Euler polygonal arcs and Subbotin's proximal aiming condition, which allows discrete trajectories to break the state constraint, evolve in its neighbourhood and then converge to it instead of staying in the state constraint set for all time.

Numerical simulation of differential-algebraic equations with embedded global optimization criteria

We are considering differential-algebraic equations with embedded optimization criteria (DAEOs), in which the embedded optimization problem is solved by global optimization. This leads to differential inclusions for cases in which there are multiple global optimizers at the same time. Jump events from one global optimum to another result in nonsmooth DAEs and reduce the order of convergence of the numerical integrator to first-order. Implementation of event detection and location as introduced in this work preserves the higher-order convergence behaviour of the integrator. This allows the computation of discrete tangent and adjoint sensitivities for optimal control problems.

On fuzzy fractional differential inclusion driven by variational–hemivariational inequality in Banach spaces

The aim of this paper is to examine an evolution problem (FFDIVHVI) involving a fuzzy fractional differential inclusion and a variational–hemivariational inequality (VHVI) in Banach spaces. First, we show a uniqueness and existence theorem for VHVI under the theory of monotone operators and the surjectivity theorem. Then, by utilizing fixed point theorem for multivalued contraction mapping and fuzzy set theory, we establish the existence result for FFDIVHVI. In addition, it is proven that the collection of all mild trajectories of FFDIVHVI exhibits compactness. Finally, we illustrate the applicability of the abstract theory by a nonlinear quasistatic thermoelastic frictional contact problem for which we provide existence results.