Fatel error with after_widget

I trying to create a simple widget to display a list of posts from a specific category, I'm getting an error log in "Notice: Undefined index: after_widget in" I also noticed a weird thing that my widget class is making all the other widgets be its child, she is not closing when the widget code is done,

This is my code ---

if ( !defined('ABSPATH') )
        die('-1');
        
        
add_action( 'widgets_init', function(){
     register_widget( 'news_roller' );
});     

function illu_news_widget(){

        wp_enqueue_style( 'your-stylesheet-name', plugins_url('/css/style.css', __FILE__), false, '1.0.0', 'all');
    }
    add_action('wp_enqueue_scripts', "illu_news_widget");

/**
 * Adds news_roller widget.
 */
class news_roller extends WP_Widget {

        /**
         * Register widget with WordPress.
         */
        function __construct() {
                parent::__construct(
                        'news_roller', // Base ID
                        __('News roller', 'isas_news'), // Name
                        array( 'description' => __( 'News roller', 'isas_news' ), ) // Args
                );
        }

        /**
         * Front-end display of widget.
         *
         * @see WP_Widget::widget()
         *
         * @param array $args     Widget arguments.
         * @param array $instance Saved values from database.
         */
        public function widget( $args, $instance ) {

                extract($args);

                // Excerpt length filter
                function new_excerpt_length($length) {
        return 10;
                }
                add_filter('excerpt_length', 'new_excerpt_length');
        
        echo $args['before_widget'];

                if ( ! empty( $instance['title'] ) ) {
                        echo $args['before_title'] . apply_filters( 'widget_title', $instance['title'] ). $args['after_title'];
                }
        if ( ! empty( $instance['cat'] ) ) {
                ?>

                                                        <ul class="illu_widget news-carousel">
                                                                <?php 
                                                                        $args = array(
                                                                                'cat' => $instance["cat"]
                                                                        );
                                                                        query_posts( $args );
                                                                        while ( have_posts() ) : the_post();
                                                                ?>
                                                                        <li>
                                                                                <a href="<?php the_permalink(); ?>">
                                                                                        <?php the_excerpt(); ?>
                                                                                </a>
                                                                        </li>
                                                                <?php 
                                                                        endwhile;
                                                                        wp_reset_query();
                                                                ?>
                                                        </ul>
        <?php 
        
        }

        echo $args['after_widget'];
                
        }

        /**
         * Back-end widget form.
         *
         * @see WP_Widget::form()
         *
         * @param array $instance Previously saved values from database.
         */

        public function form( $instance ) {
                if ( isset( $instance[ 'title' ] ) ) {
                        $title = $instance[ 'title' ];
                }
                else {
                        $title = __( 'New title', 'isas-news' );
                }
                $cat                    = $instance['cat'];
                ?>
                <p>
                        <label for="<?php echo $this->get_field_id( 'title' ); ?>">
                                <?php _e( 'Title:' ); ?>
                        </label> 
                        <input class="widefat" id="<?php 
                                echo $this->get_field_id( 'title' ); ?>" name="<?php
                                echo $this->get_field_name( 'title' ); ?>" type="text"
                                value="<?php echo esc_attr( $title ); ?>">
                </p>

                <label>
                        <?php _e( 'Category' ); ?>:
                        <?php wp_dropdown_categories( array(
                         'name' => $this->get_field_name("cat"),
                         'selected' => $instance["cat"] ) ); ?>
                </label>
      <?php
        }

        /**
         * Sanitize widget form values as they are saved.
         *
         * @see WP_Widget::update()
         *
         * @param array $new_instance Values just sent to be saved.
         * @param array $old_instance Previously saved values from database.
         *
         * @return array Updated safe values to be saved.
         */
        public function update( $new_instance, $old_instance ) {
                $instance = array();
                $instance['title'] = ( ! empty( $new_instance['title'] ) ) ? strip_tags( $new_instance['title'] ) : '';
        $instance['cat'] = ( ! empty( $new_instance['cat'] ) ) ? strip_tags( $new_instance['cat'] ) : '';
                return $instance;
        }

} // class news_roller

cant seem to figure it out, I'm must say my php is very limited.

Thanks