package Levels::Level_IV;

use strict;
use warnings;
use Math::RungeKutta;
...

sub level_iv {
    my ( $args_ref, $R, $factor, $level_iii_ref ) = @_;

    ...

    for my $i ( $t..$t_final ) {

       ...

       ( $t, $dt, @y_med ) = rk4_auto( \@y_med, \&_dydt, $t, $dt, $eps
+ );
    }

    ...

    sub _equation_air {
        my ( $args_ref, $level_iii_ref, $y ) = @_;

#I tried these options
#
#    my $_equation_air = sub {
#        my $y = shift;
#    local *_equation_air = sub {
#        my $y = shift;

        #for easy calculations make copies of the parameters (not alia
+ses)
        my arguments for formula from $args_ref and $level_iii_ref

        #differential equation for mass
        my $dydt = some formula;

        return $dydt;
    };
    
    ...

    #differential equation for fugacity at start and end times
    sub _dydt {
        my ( $t, @y ) = @_;
        my @dydt;
        
        #start differentiation at point y0 (air)
        $dydt[0] = _equation_air( $args_ref, $level_iii_ref, $y[0] );
        
        #tried these
        #$dydt[0] = _equation_air($y[0]);   #local
        #$dydt[0] = $_equation_air->($y[0]);#lexical
        
        ...

        return @dydt;
    }
    
    ...
    
    return some hash;
}
[download]

That's the original code still!! We have already told you how to fix it, and it does not give the errors you want us to look at.

However, I think I guessed what you are doing wrong: setting local *func or my $func after the point where it's used.

# BAD
sub outer {
   my $var;
   ($t, @y) = rkXXX(\@y, $dydt, $t, $dt);
   my $dydt = sub { ... };
}

# Good
sub outer {
   my $var;
   my $dydt = sub { ... };
   ($t, @y) = rkXXX(\@y, $dydt, $t, $dt);
}
[download]

I dont have all the code here but I am almost sure you are absolutely right...
Thats why it tolds me in any case undefined or empty reference...
I was not aware that I am changing semantic of "anywhere" sub to "define before use" variable with local!

Will try it out but I guess you solved my problem.