Oscillation of a Class of Fractional Differential Equations with Damping Term

Abstract

We investigate the oscillation of a class of fractional differential equations with damping term. Based on a certain variable transformation, the fractional differential equations are converted into another differential equations of integer order with respect to the new variable. Then, using Riccati transformation, inequality, and integration average technique, some new oscillatory criteria for the equations are established. As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results.

Oscillation criteria for nonlinear fractional differential equation with damping term

“…Letting ξ → b − in (34) and dividing both sides by H (ξ , c) , we obtain, On the other hand, substituting ξ with s, multiplying both sides of (33) by H (s, ξ ) and integrating it with respect to s from ξ to c for ξ ∈ (a, c] , we deduce that which contradicts (29). Thus, the proof is complete.…”

“…Recently, Qin and Zheng [29] established oscillation criteria for linear fractional di erential equations with damping term of the form:…”

Oscillation of fractional order functional differential equations with nonlinear damping

“…We will use a transformation technique also used in [28][29][30][31][32][33] in our proofs. For the sake of convenience, through the rest of this paper, we denote…”

“…Recently Feng and Meng [28], Liu, Zheng and Meng [29], Qin and Zheng [30], and Feng [31] have established some new oscillation criteria for the following equations: In this paper, we are concerned with the oscillation of fractional di erential equations with nonlinear damping terms in the form of…”

Oscillation properties of solutions of fractional neutral differential equations

“…Recently, there have been many studies concerning oscillation theory [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. However, only a few papers consider the oscillation of fractional neutral differential equations [14,15].…”