Oscillation Of Fractional Differential Equations Research Articles

On stability and oscillation of fractional differential equations with a distributed delay

In this paper, we study the stability and oscillation of fractional differential equations \begin{equation*} ^cD^\alpha x(t)+ax(t)+\int_0^1x(s+[t-1])dR(s)=0. \end{equation*} We discretize the fractional differential equation by variation of constant formula and semigroup property of Mittag-Leffler function, and get the difference equation corresponding to the integer points. From the equivalence analogy of qualitative properties between the difference equations and the original fractional differential equations, the necessary and sufficient conditions of oscillation, stability and exponential stability of the equations are obtained.

On the oscillation of fractional differential equations via \(\psi\)-Hilfer fractional derivative

On the oscillation of fractional differential equations via \(\psi\)-Hilfer fractional derivative

Forced oscillation of fractional differential equations via conformable derivatives with damping term

Based on the properties of nonlocal fractional calculus generated by conformable derivatives, we establish some sufficient conditions for oscillation of all solutions for fractional differential equations with damping term. Forced oscillation of conformable differential equations in the frame of Riemann, as well as of Caputo type, is established. Examples are provided to demonstrate the effectiveness of the main results.

On the oscillatory behavior of solutions of nonlinear fractional differential equations

The study of oscillation theory for fractional differential equations has been initiated by Grace et.al. [14]. In this paper we establish some new criteria for the oscillation of fractional differential equations with the Caputo derivative of the formcDaαx(t)=e(t)+f(t,x(t)),a>1,α∈(1,2).We also present the conditions under which all solutions of this equation are asymptotic to at + b as t → ∞ for some real numbers a, b. We shall employ a different technique rather than that in [14].

On the oscillation of fractional differential equations

Abstract 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_a^q x + f_1 (t,x) = v(t) + f_2 (t,x),\mathop {\lim }\limits_{t \to a} J_a^{1 - q} x(t) = b_1 $, where D aq 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.