Author:
George Maria Selvam A,Janagaraj R
Abstract
Abstract
In this present work, new oscillation theorems for discrete forced nonlinear equations with fractional order of the form
Δ
[
γ
(
ℓ
)
ϕ
(
u
(
ℓ
)
)
Δ
μ
(
u
(
ℓ
)
)
]
+
q
(
ℓ
)
F
[
G
(
ℓ
)
]
=
η
(
ℓ
)
,
ℓ
≥
ℓ
0
>
0
is discussed. In the above equation μ(0 < μ ≤ 1) is the fractional order,
G
(
ℓ
)
=
∑
j
=
ℓ
0
ℓ
−
1
+
μ
(
ℓ
−
j
−
1
)
(
−
μ
)
u
(
j
)
and Δ
μ
is defined as the difference operator of the Riemann Liouville (RL) derivative. Based on the properties of RL derivative, inequalities and generalized Riccati type techniques, some new sufficient conditions that are essential for the oscillation of solutions of forced fractional order discrete nonlinear equations are established.
Subject
General Physics and Astronomy
Cited by
2 articles.
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