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Mathematical Problems in Engineering
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Table of Contents
Special Issues
Mathematical Problems in Engineering
/
2010
/
Article
/
Tab 1
/
Review Article
Some Applications of Fractional Calculus in Engineering
Table 1
Fractional-order integrals of several functions.
φ
(
x
)
,
x
∈
ℜ
(
I
+
α
φ
)
(
x
)
,
x
∈
ℜ
,
α
∈
C
(
x
-
a
)
β
-
1
Γ
(
β
)
Γ
(
α
+
β
)
(
x
-
a
)
α
+
β
-
1
,
Re
(
β
)
>
0
e
λ
x
λ
-
α
e
λ
x
,
Re
(
λ
)
>
0
{
sin
(
λ
x
)
cos
(
λ
x
)
λ
-
α
{
sin
(
λ
x
-
α
π
/
2
)
,
cos
(
λ
x
-
α
π
/
2
)
,
λ
>
0
,
Re
(
α
)
>
1
e
λ
x
{
sin
(
γ
x
)
cos
(
γ
x
)
e
λ
x
(
λ
2
+
γ
2
)
α
/
2
{
sin
(
γ
x
-
α
ϕ
)
,
ϕ
=
arctan
(
γ
/
λ
)
cos
(
γ
x
-
α
ϕ
)
,
γ
>
0
,
Re
(
λ
)
>
1