It is just curious question, there is a lot of free software and scripts that serves I think all Bioinformatics research fields. Is there any field that matlab excel than these tools "actually I have never used matlab"?
Is it worth to learn it? "also there is an alternative for it Octave"
I suppose it depends on your goals. Matlab has a lot of signal/image processing functions (assuming you bought the right toolboxes), which could be useful for some people...though rarely in bioinformatics at the moment. I also found matlab useful when doing things like numerical modeling (again, not bioinformatics). Frankly, I haven't come upon an instance where I've needed matlab in years.
It used to be easier in MATLAB to create interactive plots. This is, plots were one was able to use the mouse to interactively change certain aspects of the plot, like the height and width, the x and y limits, position of the legend, ... akin of having the plot creation and and svg editor all in the same place.
R has gone a long way, but it may be that people still find it easier in MATLAB:
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version 2.3.6
So generally it is more related to pure math work not bioinformatics work "more numerical stuff "
Math or engineering I'd say. At least those are the contexts that would led themselves more toward it. An exception to this might be microarray/etc. signal deconvolution (e.g., you have an admixture and want to perform cell-type specific DE from it). While there are packages to do the deconvolution in R/Bioconductor, there are a LOT more in matlab and they use about every method one can think of, since the same math is used heavily in signal processing. You'll often find things like that implemented first in Matlab and then maybe someday (though probably never) in R.