How to delete post automatically from home page in laravel

I am trying to do delete the post on selected date but it's not working. However there is not any error, even checked with dd($request)

it's my controller,

public function save(Request $request)
    {

        $this->validate($request, [

            'content' =>'required',

            'start_date'=>'required',

            'exp_date'=>'required',

        ]);


        $save = [
            'content'=>$request->content,

            'start_date'=>Carbon::parse(strtotime($request->start_date))->format('Y-m-d'),

            'exp_date'=>Carbon::parse(strtotime($request->exp_date))->format('Y-m-d'),

        ];

       letter::create($save);

        $start_date = Carbon::parse($request->start_date)
            ->startOfDay()
            ->toDateTimeString();

        $exp_date= Carbon::parse($request->exp_date)

           ->endOfDay()

            ->toDateTimeString();

        letter::whereBetween('id', [$start_date, $exp_date])->get();

        return redirect()->back();

    }

via Chebli Mohamed