Wafa Shammakh

Model reduction of A class of Markov jump nonlinear systems with time-varying delays via projection approach

In this paper, the problem of H ∞ model reduction for a class of discrete-time Markov jump nonlinear systems with time-varying delays is investigated. Based on the Lyapunov-Krasovskii functional method, sufficient stability conditions in terms of strict LMIs are derived for the model error system. Projection approach is employed to construct a reduced-order model such that the model error system is asymptotically stable and preserves a guaranteed H ∞ performance. A numerical example is presented to illustrate the effectiveness of the developed theoretical results and to make comparisons among systems with different structures and parameters.

Three-Point Boundary Value Problems for Conformable Fractional Differential Equations

We study a fractional differential equation using a recent novel concept of fractional derivative with initial and three-point boundary conditions. We first obtain Greens function for the linear problem and then we study the nonlinear differential equation.

On Fractional Order Dengue Epidemic Model

This paper deals with the fractional order dengue epidemic model. The stability of disease-free and positive fixed points is studied. Adams-Bashforth-Moulton algorithm has been used to solve and simulate the system of differential equations.

H ∞ state estimation for discrete-time switching neural networks with persistent dwell-time switching regularities

This paper focuses on the state estimation problem for a class of discrete-time switching neural networks with persistent dwell time (PDT) switching regularities and mode-dependent time-varying delays in H ∞ sense. The considered switching regularity is more general that extends the frequently studied dwell-time (DT) and average dwell-time (ADT) switching. The random packet dropouts, which are governed by a Bernoulli distributed white sequence, are considered to exist together for the estimator design of underlying switching neural networks. The desired mode-dependent estimators are designed such that the resulting estimation error system is exponentially mean-square stable and achieves a prescribed H ∞ level of disturbance attenuation. Finally, the effectiveness and the superiority of the developed results are demonstrated through a class of synthetic oscillatory networks.

Nonlocal Integrodifferential Boundary Value Problem for Nonlinear Fractional Differential Equations on an Unbounded Domain

This paper investigates the existence of nonnegative solutions for nonlinear fractional differential equations with nonlocal fractional integrodifferential boundary conditions on an unbounded domain by means of Leray-Schauder nonlinear alternative theorem. An example is discussed for the illustration of the main work.

Resilient model approximation for Markov jump time-delay systems via reduced model with hierarchical Markov chains

ABSTRACT In this paper, the resilient model approximation problem for a class of discrete-time Markov jump time-delay systems with input sector-bounded nonlinearities is investigated. A linearised reduced-order model is determined with mode changes subject to domination by a hierarchical Markov chain containing two different nonhomogeneous Markov chains. Hence, the reduced-order model obtained not only reflects the dependence of the original systems but also model external influence that is related to the mode changes of the original system. Sufficient conditions formulated in terms of bilinear matrix inequalities for the existence of such models are established, such that the resulting error system is stochastically stable and has a guaranteed l2-l∞ error performance. A linear matrix inequalities optimisation coupled with line search is exploited to solve for the corresponding reduced-order systems. The potential and effectiveness of the developed theoretical results are demonstrated via a numerical example.

Positive Solutions for Nonlinear -Fractional Difference Eigenvalue Problem with Nonlocal Conditions

The problem of positive solutions for nonlinear -fractional difference eigenvalue problem with nonlocal boundary conditions is investigated. Based on the fixed point index theory in cones, sufficient existence of positive solutions conditions is derived for the problem.

A Study of Caputo-Hadamard-Type Fractional Differential Equations with Nonlocal Boundary Conditions

Existence and uniqueness results of positive solutions to nonlinear boundary value problems for Caputo-Hadamard fractional differential equations by using some fixed point theorems are presented. The related Green’s function for the boundary value problem is given, and some useful properties of Green’s function are obtained. Example is presented to illustrate the main results.

Fuzzy soft set over a fuzzy topological space

AbstractThe aim of this article, we combine the fuzzy soft set and fuzzy topological space. We introduce the notion of fuzzy soft set over common universe of fuzzy topological space. We defined quasi-open fuzzy soft set over fuzzy topological space and we study the properties of extended union of two quasi-open fuzzy soft set over fuzzy topological space. We study “OR” and “AND” operations of quasi-open fuzzy soft set over fuzzy topological space. We also define open fuzzy soft set, b-open fuzzy soft set and b-closed fuzzy soft set over fuzzy topological space. We give some characterizations of these concepts.