This work deals with a parabolic chemotaxis model nonlinear diffusion and nonlocal reaction source. The problem is formulated on the whole space and, depending specific interplay between coefficients associated to such reaction, we establish that all given solutions are uniformly bounded in time. To be precise, study these attractive (sign ``$+$'') repulsive ``$-$'') following models, formally described by Cauchy problems \begin{equation}\label{problem_abstract} \tag{$\Diamond$}...

This paper is framed in a series of studies on attraction-repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities logistic sources, for the dynamics cell density, consumption and/or production impacts, those chemicals. In particular, herein we focus situation where signal responsible gathering tendencies particles' distribution produced, while opposite counterpart consumed. such sense, this research complements two recent results, chemicals evolve...

ABSTRACT We study a class of zero‐flux attraction–repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion cell density , chemosensitivities and production rates chemoattractant chemorepellent . In addition, source involving also gradient is incorporated. Our overall touches on different aspects: we address questions connected to local well‐posedness, derive sufficient conditions ensure boundedness solutions, finally, develop numerical simulations giving insights...

This paper is devoted to investigate synchronization and antisynchronization of N ‐coupled general fractional‐order complex chaotic systems described by a unified mathematical expression with ring connection. By means the direct design method, appropriate controllers are designed transform error dynamical system into nonlinear antisymmetric structure. Thus, using recently established result for Caputo fractional derivative quadratic function extension Lyapunov several stability criteria...

In this article, we prove that the ω-periodic discrete evolution family $\Gamma:= \{\rho(n,k): n, k \in\mathbb{Z}_{+}, n\geq k\}$ of bounded linear operators is Hyers-Ulam stable if and only it uniformly exponentially under certain conditions. More precisely, for each real number γ sequence $(\xi(n))$ taken from some Banach space, approximate solution nonautonomous system $\theta _{n+1} = \Lambda_{n}\theta_{n}$ , $n\in\mathbb{Z}_{+}$ represented by $\phi...

Abstract This paper discusses the synchronization problem of N -coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On basis direct design method, we appropriate controllers to transform error dynamical system into a nonlinear antisymmetric structure. By choosing Lyapunov functions and employing Lyapunov-based stability theory, several sufficient conditions are obtained ensure asymptotical stabilization at origin. The proposed method is universal,...

We enter the details of two recent articles concerning as many chemotaxis models, one nonlinear and other linear, both with produced chemoattractant saturated chemorepellent. These works, when properly analyzed, leave open room for some improvement their results. generalize outcomes mentioned articles, establish statements put all claims together; in particular, we select sharpest ones schematize them. Moreover, complement our research also logistic sources are considered overall study.

For nth order linear homogeneous and nonhomogeneous differential equations with nonconstant coefficients, we prove Hyers-Ulam stability by using open mapping theorem.The generalized is also investigated.

In this paper, we interrogate different Ulam type stabilities, ie, β –Ulam–Hyers stability, generalized –Ulam–Hyers–Rassias and for n th order nonlinear differential equations with integrable impulses of fractional type. The existence uniqueness solutions are investigated by using the Banach contraction principle. end, give an example to support our main result.

We prove that the system $\dot{\theta}(t) =\Lambda(t)\theta(t)$ , $t\in\mathbb{R}_{+}$ is Hyers-Ulam stable if and only it uniformly exponentially under certain conditions; we take exact solutions of Cauchy problem $\dot{\phi}(t)=\Lambda(t)\phi(t)+e^{i\gamma t}\xi(t)$ $\phi(0)=\theta_{0}$ as approximate $\dot{\theta}(t)=\Lambda(t)\theta(t)$ where γ any real number, ξ a 2-periodic, continuous, bounded vectorial function with $\xi(0)=0$ $\Lambda(t)$ 2-periodic square matrix order l.

We study a two-dimensional boundary value problem described by tensorial equation in bounded domain. Once its more general definition is given, we conclude that analysis linked to the resolution of an overdetermined hyperbolic and hence present some discussions considerations. Secondly, for simplified version original formulation, which leads degenerate on rectangle, prove existence uniqueness solution under proper assumptions data.

In this paper, we introduce and investigate the concepts of conformable delta fractional derivative integral on time scales.Basic properties theory are proved.

Abstract In this paper we study existence and uniqueness of solutions for a coupled system consisting fractional differential equations Caputo type, subject to Riemann–Liouville integral boundary conditions. The is established by Banach contraction principle, while the derived Leray–Schauder’s alternative. We also Hyers–Ulam stability mentioned system. At end, examples are presented which illustrate our results.

With the development of science and technology, application chaos theory in various fields is increasingly receiving attention.Especially medical field, provides new theories methods for disease prediction, diagnosis, treatment, other aspects.This article first briefly reviews theory, followed by a comparative study numerical solutions Lorentz model.Finally, focuses on practical practice, looks forward to future trend emphasizes enormous potential personalized medicine, precision fields.

Abstract In this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe existence uniqueness solutions for proposed model. model contains both integer derivatives. Thus, exponential function...

In this paper, we are dedicated to an SIS reaction-diffusion-chemotaxis epidemic model with cross-diffusion including gradient-dependent flux limitation and standard incidence in spatially heterogeneous environments. We first establish the existence of globally bounded classical solution corresponding Neumann initial-boundary value problem for arbitrary reasonably regular initial data. Moreover, data small size, a result concerning global solvability is obtained provided that space-dependent...

This paper is concerned with adaptive control for anti-synchronization of a class uncertain fractional-order chaotic complex systems described by unified mathematical expression.By utilizing the recently established result Caputo fractional derivative quadratic function and employing technique, we design controllers some parameter update laws to anti-synchronize two unknown parameters.The proposed method has generality, simplicity, feasibility.Moreover, between Lorenz system L ü implemented...

We study some attraction repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of cell density, and chemosensitivities production rates chemoattractant chemorepellent. Additionally, a source also involving expression gradient species is incorporated.