Route::post('update_article/{id}', 'ArticleController@update_article')->name('articles.update');

{!! Form::model($article, ['route'=>['articles.update', $article->id], 'method' => 'post', 'class' => 'form-horizontal form-stripe']) !!}

public function update_article(Request $request, $id)
    {
        $data = Article::find($id);
        $url = $this->url->to('/');
        $data->image = $request->input('image');
        $data->title = $request->input('title');
        $data->description = $request->input('description');
        $data->user_id = Auth::id();
        $data->status = $request->input('status');


       if ($request->hasFile('image'))
       {
        $f_imageName = time().'.'.request()->image->getClientOriginalExtension();
        request()->image->move(public_path('uploads/articles'), $f_imageName);
        $data->image =$url.'/public/uploads/articles/'.$f_imageName;
       }
       else
       {
        $data->image = $request->input('image_hidden');
       }

    $data->save();
    Session::flash('success', 'articles has been updated');
    return redirect()->route('articles.index');
    }

Route::resource('articles', 'ArticleController');

if you have created the resource as you mentioned.
Route::resource('articles', 'ArticleController');

then remove the following code from your route ( web.php ) and run the code.
Route::post('update_article/{id}', 'ArticleController@update_article')->name('articles.update');