why not sourcing your .bashrc (or anywhere you define your alias) before calling the alias?

perl -e 'system("source ~/.profile; source ~/.bashrc; bash --login -c 
+l");'
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For instance, matlab is an alias for me defined in ~/.profile. Try to check if matlab exist as a command from perl:

$perl -e 'system("command -v matlab")'

$perl -e 'system("source ~/.profile;command -v matlab")'
alias matlab='/Applications/MATLAB_R2015a.app/bin/matlab'
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Best, Hatef