None of these alignment algorithms are included in Matlab.
Do not mix the "fasta" alignment algorithm with the "fasta" file format. Matlab provides fastaread and fastawrite for I/O FASTA formatted files.
In the case of the "blast" algorithm Matlab does provides a wrapper that allows you to pass the information to a locally installed blast (blastlocal), and provides a read function (blastlocalread) that will let you put the results of the alignments back in Matlab, but you will need to install the blast algorithm (provided by NCBI) by yourself. Also Matlab provides a function that allows you to submit queries to the NCBI's blast server, balstncbi (i.e. aligning against their databases). The function blastread will read the web data back into Matlab.