Javascript/Jquery??

Hi, I’ve been working on a side nav for my post categories. The theme that I have been modifying ‘comfy’ uses JQuery and I think this is effecting the javascript for my side menu from working. Please take a look at the menu I’ve made; https://www.fuximagazine.com/film/2010/05/17/japan-to-remake-90s-box-office-mega-hit-ghost/

The options on the left should work as an expanding/collapsing menu. Below is the script that I am using;

function initMenus() {
	$('#fuximenu ul').hide();
	$.each($('#fuximenu'), function(){
		$('#' + this.id + '.expandfirst ul:first').show();
	});
	$('#fuximenu li a').click(
		function() {
			var checkElement = $(this).next();
			var parent = this.parentNode.parentNode.id;

			if($('#' + parent).hasClass('noaccordion')) {
				$(this).next().slideToggle('normal');
				return false;
			}
			if((checkElement.is('ul')) && (checkElement.is(':visible'))) {
				if($('#' + parent).hasClass('collapsible')) {
					$('#' + parent + ' ul:visible').slideUp('normal');
				}
				return false;
			}
			if((checkElement.is('ul')) && (!checkElement.is(':visible'))) {
				$('#' + parent + ' ul:visible').slideUp('normal');
				checkElement.slideDown('normal');
				return false;
			}
		}
	);
}

I think because it starts with ‘function’ is what is stopping it working. My other menu script, along with other scripts start with a $, in a file called jquery-custom.js

Does anybody have any idea how I can tell if this is case? or how you can edit javascript to become jquery?

Thanks in advance.