Edit in JSFiddle

var  app  =  new  Vue ({
		el:  '#app',
		data: {
			heading:  'VoidCanvas Online Library',
			heading_Color:'headingColor',
			booksFontSize:'booksFontSize',
			author:'author',
			searchString:  '',
			books: [
				{
				title:  'Elon Musk',
				by:'Ashlee Vance',
				url:'http://www.voidcanvas.com/'
				},
				{
				title:  'Steve Jobs',
				by:'George Llian',
				url:'http://www.voidcanvas.com/'
				},
				{
				title:  'Face of Facebook',
				by:  'Sandip Paul',
				url:'http://www.voidcanvas.com/'
				},
				{
				title:  'Tim Cook',
				by:'Andy Atkins',
				url:'http://www.voidcanvas.com/'
				},
				{
				title:  'Abdul Kalam',
				by:'Arun Tiwari',
				url:'http://www.voidcanvas.com/'
				},
				{
				title:  'Story of Elon Musk',
				by:'BP John',
				url:'http://www.voidcanvas.com/'
				},
				{
				title:  'Story of Bill Gates',
				by:'Russel Crook',
				url:'http://www.voidcanvas.com/'
				},
				{
				title:  'Becoming Steve Jobs',
				by:'Andrew Russel',
				url:'http://www.voidcanvas.com/'
				}
			]
			},
		computed: {
			filteredBooks:  function () {
				var  books_array  =  this.books,
				searchString  =  this.searchString;
				if(!searchString) {
					return  books_array;
				}
				searchString  =  searchString.trim().toLowerCase();
				books_array  =  books_array.filter(function(item) {
					if(item.title.toLowerCase().indexOf(searchString) !==  -1) {
					return  item;
					}
				});
				return  books_array;
		}
		}
	});
<html>

  <head>
    <link rel="stylesheet" href="./cssfile.css">
  </head>

  <body>
    <div id="app">
      <b v-bind:class="heading_Color"> {{heading}} </b>
      <input type="text" v-model="searchString" placeholder="search box" />
      <div class="design">
        <ul style="list-style: none;">
          <li v-for="book in filteredBooks">
            <a v-bind:href="book.url">{{book.title}} -by- {{book.by}}</a>
          </li>
        </ul>
      </div>
    </div>

    <script src="./vue.js"></script>
    <script src="./vueTry.js"></script>
  </body>

</html>
body {
  background-color: #dbd8d8
}

.headingColor {
  color: purple;
  margin-left: 120px;
}

input {
  width: 300px;
  margin-left: 80px;
}

.design {
  width: 400px;
  margin-left: 10px
}

.design a {
  position: relative;
  display: block;
  padding: .4em .4em .4em 2em;
  *padding: .4em;
  margin: .5em 0;
  border: 3px solid white;
  background: #FC756F;
  color: #444;
  text-decoration: none;
  transition: all .2s ease-in-out;
}

.design a:hover {
  background: #d6d4d4;
  text-decoration: none;
  transform: scale(1.1);
}

.design a:before {
  position: absolute;
  left: -1.3em;
  top: 50%;
  margin-top: -1.3em;
  background: #FC756F;
  height: 2em;
  width: 2em;
  line-height: 2em;
  border: .3em solid #fff;
  text-align: center;
  font-weight: bold;
  color: #FFF;
}