On the Oscillation of Fractional Differential Equations
نویسنده
چکیده
In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form D ax+ f1(t, x) = v(t) + f2(t, x), lim t→a+ J1−q a x(t) = b1, where D a denotes the Riemann-Liouville differential operator of order q, 0 < q ≤ 1. The results are also stated when the Riemann-Liouville differential operator is replaced by Caputo’s differential operator. MSC 2010 : Primary 34A08: Secondary 34C10, 26A33
منابع مشابه
Study on stability analysis of distributed order fractional differential equations with a new approach
The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...
متن کاملCascade of Fractional Differential Equations and Generalized Mittag-Leffler Stability
This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...
متن کاملBasic results on distributed order fractional hybrid differential equations with linear perturbations
In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...
متن کاملA Numerical Method for Solving Fuzzy Differential Equations With Fractional Order
In this paper we present a numerical method for fuzzy differential equation of fractional order under gH-fractional Caputo differentiability. The main idea of this method is to approximate the solution of fuzzy fractional differential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.
متن کاملOn the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales
n this paper, at first the concept of Caputo fractionalderivative is generalized on time scales. Then the fractional orderdifferential equations are introduced on time scales. Finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.
متن کاملPresentation of two models for the numerical analysis of fractional integro-differential equations and their comparison
In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...
متن کامل