Here is an easy way to get very close to what you want. The '>' is removed from the start of every line and it is added to the end of every line (except the last).

use strict;
use warnings;
use Data::Dumper;

my $filename = 'file.fasta';
 
open( my $MY_HANDLE, '<', $filename ) or die "Couldn't open file";

(undef, my @chars) = do{local $/="\n>"; <$MY_HANDLE>};
print Dumper(\@chars);
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OUTPUT:

$VAR1 = [
          'NM_001198855.1 Homo sapiens cytochrome P450 family 2 subfam
+ily C memb
er 8 (CYP2C8)
ACATGTCAAAGAGACACACACTAAATTAGCAGGGAGTGTTATAAAAACTTTGGAGTGCAAGCTCACAGCT
GTCTTAATAAGAAGAGAAGGCTTCAATGGAACCTTTTGTGGTCCTGGTGCTGTGTCTCTCTTTTATGCTT
CTCTTTTCACTCTGGAGACAGAGCTGTAGGAGAAGGAAGCTCCCTCCTGGCCCCACTCCTCTTCCTATTA
>',
          'NR_029834.1 Homo sapiens microRNA 200a (MIR200A), microRNA
CCGGGCCCCTGTGAGCATCTTACCGGACAGTGCTGGATTTCCCAGCTTGACTCTAACACTGTCTGGTAAC
GATGTTCAAAGGTGACCCGC
>',
          'AC067940.1 Homo sapiens clone RP11-818E9, LOW-PASS SEQUENCE
+ SAMPLING
AAATACAACTTTAAATCAAAACGGTAAAAATTCCACTCTTTCATACTAACTTCAAAAGTATTTGCTTTAA
AAAAAAAGNNNNNNNNNNAAACTGAATTTCTATTAAGCATCTATTTATAGAAGAGAGTAAACACCCCGTG
AATAAAAGACAGAGAATTGTAGCAGCCCGAAGTCCCTTTTCTCTCCTCCCAAGCATTTGGCTCTGGTCCA
AATTCACATATCCTGCTCCGTAAAACAAAGTGCCTTGGTTAACCTAACGTTATTCCTTGAACAGTAGTTT
AGTGATCAACTAGTTTTTGTTGTTGTTGTTGTTTGAGACAGAGTCTCACTCTGTCGCCCAGGCTGGAGTG
CAGTGGCGAGATCTCAGCTCACTGCAACCTCTGCTGCCCAGGTTCAAGGGATTCTCCTGCCTCAGCCTCC
CAAGTAGCTGGTATTACAGGCACCTGCCACCGCGCCTGGCTAATTTTTTTTTTTTTTTTTTTTTGTATTT
'
        ];
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I also recommend that you check CPAN for modules that help with parsing fasta files. Sorry, I cannot offer more specific help.