Recently several authors have started to examine qualitative properties of fractional equations and among them, some have devoted their attention to equations with the so called modified Riemann-Liouville derivative, which was established by Jumarie. Their results utilize nice properties of Jumarie operator and in fact convert statements from integer order differential equations to those with Jumarie derivative. The aim of this paper is to give a survey of existing results and comment on the possibility of getting similar results when converting from half-linear criteria.

1.
D.
Chen
,
Oscillation criteria of fractional differential equations
,
Adv. Differ. Equ.
,
33
,
1
18
(
2012
).
2.
D.
Chen
,
Oscillatory behavior of a class of fractional differential equations with damping
,
U. P. B. Sci. Bull.
,
75
,
107
118
(
2013
).
3.
Q.
Feng
,
F.
Meng
,
Oscillation Solutions to nonlinear forced fractional differential equations
,
Electronic Journal of Differential Equations
,
169
,
1
10
(
2013
).
4.
Z.
Han
,
Y.
Zhao
,
Y.
Sun
,
C.
Zhang
,
Oscillation for a class of fractional differential equations
,
Discrete Dyn. Nat. Soc.
, ID
390282
,
1
6
(
2013
).
5.
T.
Liu
,
B.
Zheng
,
F.
Meng
,
Oscillation on a class of differential equations of fractional order
,
Math. Probl. Eng.
, ID
830836
,
1
12
(
2013
).
6.
V.
Ganesan
,
M. Sathish
Kumar
,
Oscillation Theorems for Fractional Order Neutral Differential Equations
,
Journal of Applied Computer Science ’ Mathematics
, 2/2016,
10
(
22
),
46
51
(
2016
).
7.
S. R.
Grace
,
R. P.
Agarwal
,
J. Y.
Wong
,
A.
Zafer
,
On the oscillation of fractional differential equations
,
Frac. Calc. Appl. Anal.
,
15
,
222
231
(
2012
).
8.
G.
Jumarie
,
Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results
,
Computers ’ Mathematics with Applications
,
51
(
9
),
1367
1376
(
2006
).
9.
K. S.
Miller
,
B.
Ross
,
An introduction to the fractional calculus and fractional differential equations
,
1993
.
10.
I.
Podlubny
,
Fractional Differential Equations
,
Academic Press, San Diego
,
1999
.
11.
V. E.
Tarasov
,
No violation of the Leibniz rule. No fractional derivative
,
Commun Nonlinear Sci Numer Simulat
18
,
2945
2948
(
2013
).
12.
Y. Z.
Wang
,
Z. L.
Han
,
P.
Zhao
,
S. R.
Sun
,
On the oscillation and asymptotic behavior for a kind of fractional differential equations
,
Adv. Differ. Equ.
,
50
,
1
11
(
2014
).
13.
Y. Z.
Wang
,
Z. L.
Han
,
P.
Zhao
,
S. R.
Sun
,
Oscillation theorems for fractional neutral differential equations
,
Hacettepe Journal of Mathematics and Statistics
,
44
(
6
),
1477
1488
(
2015
).
14.
R.
Xu
,
Oscillation criteria for nonlinear fractional differential equations
,
Journal of Applied Mathematics
, ID
971357
,
1
7
(
2013
).
15.
B.
Zheng
,
Oscillation for a class of nonlinear fractional differential equations with damping term
,
J. Adv. Math. Stud.
,
6
,
107
115
(
2013
).
This content is only available via PDF.
You do not currently have access to this content.