how to update a particular session array value in laravel

My cart session is

Array
(
    [id] => 123-XL
    [prod_name] => Classic Polo Grey Shirt
    [prod_rate] => 2100
    [size] => XL
    [qty] => 1
    [ind_tot] => 2100
)
 
Array
(
    [id] => 213-32
    [prod_name] => LP_Pant
    [prod_rate] => 2800
    [size] => 32
    [qty] => 1
    [ind_tot] => 2800
)

and my ajax code is

$(document).ready(function(){
        $('.incr').click(function (event) {
            event.preventDefault();
            $id=this.id;
            $rate= $("#rate"+$id).html();
            $qty = $("#qty"+$id).val();
            $ind_tot = $("#ind_tot"+$id).html();
            //alert($qty);
            $.ajax({
                url:"", 
                dataType:"json",
                type:"post",
                data:{
                id:$id,
                rate:$rate,
                qty:$qty,
                ind_tot:$ind_tot,
                "_token": "",
                },
                success: function(result){
                    alert(result); 
                }
            });

and my increment function is

public function increment(Request $request){
    $id = $request->id;
    $rate = $request->rate;
    $qty = $request->qty;
    $ind_tot = $request->ind_tot;
    foreach (Session::get('cart_sess') as $cart_items => $cart_item) {
        if($cart_item['id']==$id){
            $qty_up = $qty +1;
            Session::put($cart_item['qty'], $qty_up);
        }
    }
    return response()->json($qty_up, 200);  
} 

help me to to fix the code, how can i update the qty of particular id, how to update a particular value of array session in laravel

also help me to how json response can be send and how json request can be decode in ajax function

via Chebli Mohamed