Convert Gregorian date to solar in WordPress

I have included a code snippet in the functions.php file that converts the Gregorian date to solar.

I use the following shortcode to display the publication date of my posts, which correctly converts from Gregorian to Solar:

<?php the_time('Y/m/d'); ?> 

I also use the following shortcode to display my posts updates:

<?php the_modified_time('Y/m/d'); ?>

The date conversion code for this shortcode doesn't work and still shows me Gregorian date.

Is it possible to edit this code so that the shortcode also supports updating the date and converts it to solar date?

The code I put in the functions.php file:

add_filter('the_time', 'change_date_format');

function change_date_format(){
    //change date language here
    $date = get_the_time('Y/m/d');
    $date = explode('/', $date);
    $farsi_date = g2p($date[0],$date[1],$date[2]);
    return $farsi_date[0].'/'.$farsi_date[1].'/'.$farsi_date[2];
}

function g2p($g_y, $g_m, $g_d)
{
    $g_days_in_month = array(31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31);
    $j_days_in_month = array(31, 31, 31, 31, 31, 31, 30, 30, 30, 30, 30, 29);

    $gy = $g_y-1600;
    $gm = $g_m-1;
    $gd = $g_d-1;

    $g_day_no = 365*$gy+floor(($gy+3)/4)-floor(($gy+99)/100)+floor(($gy+399)/400);

    for ($i=0; $i < $gm; ++$i){
        $g_day_no += $g_days_in_month[$i];
    }

    if ($gm>1 && (($gy%4==0 && $gy%100!=0) || ($gy%400==0))){
        /* leap and after Feb */
        ++$g_day_no;
    }

    $g_day_no += $gd;
    $j_day_no = $g_day_no-79;
    $j_np = floor($j_day_no/12053);
    $j_day_no %= 12053;
    $jy = 979+33*$j_np+4*floor($j_day_no/1461);
    $j_day_no %= 1461;

    if ($j_day_no >= 366) {
        $jy += floor(($j_day_no-1)/365);
        $j_day_no = ($j_day_no-1)%365;
    }
    $j_all_days = $j_day_no+1;

    for ($i = 0; $i < 11 && $j_day_no >= $j_days_in_month[$i]; ++$i) {
        $j_day_no -= $j_days_in_month[$i];
    }

    $jm = $i+1;
    $jd = $j_day_no+1;

    return array($jy, $jm, $jd, $j_all_days);
}

Hook another filter with the same filter function you already use.

add_filter('the_modified_time', 'change_date_format');