Vue-Laravel form Submission

Change your script to the following and try not to use any reserved keywords.

new Vue({
    router,
    components: [AdviceForm],
}).$mount('#app');

<script>
  export default {
    name: "AdviceForm",
    // data should be function outside the 
    // methods and try a non reserved keyword.
    data: function() {
      return {
        form_name: ''
      };
    },
    methods: {
       // All the methods
    },
    components: []
  };
</script>