Try:

distFunckappa = ((v^2/(k - 3/2) + 1)^-k Gamma[k + 1] v^2)/(k Sqrt[(k - 3/2) \[Pi]] Gamma[k - 0.5])
k = 2;

ListLogLogPlot[Table[{v, distFunckappa}, {v, 0.1, 10, 1/10}], 
PlotStyle -> Directive[Blue, Thick], 
AxesStyle -> Directive[Black, Bold, FontSize -> 14], 
TicksStyle -> Directive[Black, Bold], AxesLabel -> {"v", "DNF"}, Joined -> True]

Probably a bug in LogLogPlot in Mathematica 11.0.0.

Try plot in Plot:

 Plot[(0.900316*v^2)/(1 + 2 v^2)^2, {v, 0, 10}]

And what Yours conclusions ?

Mathematica 10.2.

Mathematica 11.3.

My version of Mathematica is Mathematica 11.0. It gives me the first plot and matlab gives me the second plot and Matlab is correct. But people using Mathematica 11.3 is getting the same plot as matlab