R-boundedness Approach to linear third differential equations in a UMD Space

The aim of this work is to study the existence of a periodic solutions of third order differential equations $z'''(t) = Az(t) + f(t)$ with the periodic condition $x(0) = x(2\pi), x'(0) = x'(2\pi)$ and $x''(0) = x''(2\pi)$. Our approach is based on the R-boundedness and $L^{p}$-multiplier of linear operators

SOLVING HYBRID FUZZY FRACTIONAL DIFFERENTIAL EQUATIONS BY IMPROVED EULER METHOD

In this paper we study numerical methods for hybrid fuzzy fractional differential equations and the iteration method is used to solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition. We consider a differential equation of fractional order  and we compared the results with their exact solutions in order to demonstrate the validity and applicability of the method. We further give the definition of the Degree of Sub element hood of hybrid fuzzy fractional differential equations with examples.

Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality

This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems

SOLVING SECOND ORDER HYBRID FUZZY FRACTIONAL DIFFERENTIAL EQUATIONS BY RUNGE KUTTA 4TH ORDER METHOD

In this paper we study numerical methods for second order hybrid fuzzy fractional differential equations and the variational iteration method is used to solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition. We consider a second differential equation of fractional order and we compared the results with their exact solutions in order to demonstrate the validity and applicability of the method. We further give the definition of the Degree of Sub element hood of hybrid fuzzy fractional differential equations with examples.   Keywords: hybrid fuzzy fractional differential equations, Degree of Sub Element Hoo

Razumikhin Stability Theorem for Fractional Systems with Delay

Fractional calculus techniques and methods started to be applied successfully during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional-order nonlinear time-delay systems for Riemann-Liouville and Caputo derivatives and we extended Razumikhin theorem for the fractional nonlinear time-delay systems

Finite Time Stability Criteria for Nonlinear Fractional Order Dynamical System

In this paper finite time stability criteria for a class of nonlinear fractional order delayed system is addressed. By using the generalized and classical Bellman-Gronwall’s approach sufficient conditions that guarantees system trajectories to stay within the a priori given set is obtained. Keywords: Nonlinear system, multiple time delays, Finite time stability, fractional order syste

Global output feedback stabilization for nonlinear fractional order time delay systems

summary:This paper investigates the problem of global stabilization by state and output-feedback for a family of for nonlinear Riemann-Liouville and Caputo fractional order time delay systems written in triangular form satisfying linear growth conditions. By constructing a appropriate Lyapunov-Krasovskii functional, global asymptotic stability of the closed-loop systems is achieved. Moreover, sufficient conditions for the stability, for the particular class of fractional order time-delay system are obtained. Finally, simulation results dealing with typical bioreactor example, are given to illustrate that the proposed design procedures are very efficient and simple

Non-Lyapunov stability of the fractional-order time-varying delay systems

U ovom radu, kriterijumi stabilnosti na konačnom vremenskom intervalu su prošireni na nelinearne nehomogene perturbovane sisteme necelobrojnog reda koji sadrže višestruka vremenski promenljiva kašnjenja. Dobijeni su dovoljni uslovi stabilnosti za sisteme necelog reda sa višestrukim vremenskim kašnjenjima korišćenjem generalizovanog i klasičnog Gronwallovog pristupa. Numerički primer je dat u cilju ilustracije značaja dobijenog rezultata.In this paper, the finite-time stability criteria are extended to nonlinear nonhomogeneous perturbed fractional-order systems including multiple time-varying delays. The sufficient conditions of a stability for the fractional systems with multiple time delays are obtained by using the generalized and classical Gronwall's approach. A numerical example is presented to illustrate the validity of the obtained result

Closed-loop iterative learning control for fractional-order linear singular time-delay system: PDα-type

U ovom radu razmatrano je iterativno upravljanje učenjem u zatvorenoj petlji (ILC) - PDα tip linearnim singularnim sistemom sa kašnjenjem necelog reda. Dati su dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PD-alfa tipa ILC za datu klasu linearnog singularnog sistema sa kašnjenjem necelog reda zajedno sa odgovarajućom teoremom i dokazom. Takođe, po prvi put je u ovom radu predloženi tip PDα ILC primenjen za datu klasu linearnih singularnih sistema sa kašnjenjem necelog reda sa neizvesnošću. Konačno, valjanost predloženog ILC algoritma upravljanja za razmatranu klasu singularnih sistema je potvrđena sa adekvatnom numeričkom simulacijom.In this paper a closed-loop PDα - type iterative learning control (ILC) of fractional order linear singular time-delay system is considered. The sufficient conditions for the convergence in time domain of the proposed PD-alpha type ILC for a class of fractional order singular system are given by the corresponding theorem together with its proof. Also, for the first time, we proposed a proposed ILC PDα type for a given class of uncertain, fractional order, singular systems. Finally, the validity of the proposed PDα ILC scheme for a class of fractional order singular time-delay system is verified by a numerical example