Basic Examples (6)
Basic Examples
(6)
Calculate the half-order conformable fractional derivative of a quadratic function with respect to :
x
In[104]:=
Out[104]=
x
In general, for , we have:
0<α<1
In[105]:=
Assuming{α∈Reals,0<α<1},Simplify@[x,{x,α}]
Out[105]=
1-α
x
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Arbitrary-order fractional derivative of a function in :
x
In[106]:=
Out[106]=
-α+Max[1,Ceiling[α]]
x
(Max[1,Ceiling[α]])
f
Plot these for :
f(x)=
2
x
In[107]:=
PlotEvaluate@Table[,{x,α}],{α,{0,1/2,9/10,1}},{x,0,1},PlotLegends->Thread[α=={0,1/2,9/10,1}]
2
x
Out[107]=
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Conformable fractional derivative of :
In[108]:=
fr=Table[Sin[x],{x,α}],{α,{1/2,9/10,2.5,3.5}}
Out[108]=
Cos[x],-Cos[x],Sin[x]
x
Cos[x],1/10
x
0.5
x
0.5
x
In[109]:=
Plot[fr,{x,0,10π}]
Out[109]=
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Conformable fractional derivative of :
In[67]:=
Out[67]=
0.2
x
a
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Conformable fractional derivative of at various values of :
m
In[68]:=
Table[JacobiSN[u,m],{u,α}],{α,0,1,1/3}
Out[68]=
JacobiSN[u,m],JacobiCN[u,m]JacobiDN[u,m],JacobiCN[u,m]JacobiDN[u,m],JacobiCN[u,m]JacobiDN[u,m]
2/3
u
1/3
u
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Conformable fractional derivative of some transcedental functions:
In[69]:=
Out[69]=
,
,Sinhx+πCeiling[α]
x
-α+Ceiling[α]
x
-α+Ceiling[α]
x
|
Ceiling[α]
(-)
-α+Ceiling[α]
x
1
2
Scope (5)
Scope
(5)
Options (2)
Options
(2)
Applications (1)
Applications
(1)
Properties and Relations (2)
Properties and Relations
(2)