Three-dimensional fractional system with the stability condition and chaos control

Abstract

A three-dimensional system is introduced in this paper and its local stability is analyzed. Our study establishes the validity and uniqueness of the linear feedback control for the proposed system and proves its existence and uniqueness. The numerical simulation algorithm described by Atanackovic and Stankovic is finally applied. The analytical results are analyzed and the dynamics of the system are explored in more detail.

Set-valued analysis of anti-angiogenic therapy and radiotherapy

“…Proposition 1 Assume that there exists θ ∈ R * + such that (p 0 , q 0 , r 0 , w 0 ) ∈ D θ , and (u, v) solution to the viability problem (5), then (u, w) solves the control problem (2).…”

“…[4] Considers a fractional-order HIV epidemic model, and determines the positivity and boundedness of the solution and the stability conditions of the model, and discusses the global dynamics of the endemic equilibrium point, by using Lyapunov functional approach. [5] Employs the feedback control on a chaotic system with fractional-order. [6] Proposes a Caputo HIV-1 model incorporating AIDS-infected cancer cells, and investigates the existence and uniqueness of its solutions via fixed point theory, and performs the stability analysis of the model.…”

Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption

“…Obviously, this feature is very relevant for modeling the spread of infections [18,19,20,21,22,23,24]. For this reason, many researchers have adopted this analytical vision [25,26,27,28,29,30,31]. In [32], the authors derived a non-integer order system for the co-infection mechanisms.…”

Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays

“…Many problems in viscoelasticity, acoustics, populations dynamics, electromagnetics, hydrology, chemical reactions and other areas can be modeled by fractional integro-differential equations; see [30][31][32] and references therein. For example, take the the nonlinear oscillation of earthquake model, fluid-dynamic traffic model, secondgrade fluid model, circulant Halvorsen system, susceptible-infected-recovered epidemic model with a fractional derivative and many other recent developments in the description of anomalous by fractional dynamics; see [33][34][35][36].…”