<div class="reviews__carousel owl-carousel owl-theme">
  <div class="reviews__card">
    отзыв
  </div>
  <!-- /card -->
  <div class="reviews__card">
    отзыв
  </div>
  <!-- /card -->
  <div class="reviews__card">
    отзыв
  </div>
  <!-- /card -->
  <div class="reviews__card">
    отзыв
  </div>
  <!-- /card -->
  <div class="reviews__card">
    отзыв
  </div>
  <!-- /card -->
  <div class="reviews__card">
    отзыв
  </div>
  <!-- /card -->
  <div class="reviews__card">
    отзыв
  </div>
  <!-- /card -->
</div>

<div class="reviews__arrows">
  <button class="arrows arrows_prev">
    Prev
  </button>
  <button class="arrows arrows_next">
    Next
  </button>
</div>

.reviews__arrows {
  text-align: center;
  padding: 10px;
}
.reviews__card {
  background: #444;
  color: #fff;
  padding: 20px;
  text-align: center;
}
.arrows.disabled {
  pointer-events: none;
  background-color: #eee;
  color: #bdbdbd;
  border-color: #eee;
  box-shadow: none;
}

$(document).ready(function(){
  var carousel = $(".reviews__carousel");

 /***function***/
function DisableBtn() {
    var firstslide = $(".owl-stage .owl-item:first-child").hasClass("active");
  var lastslide = $(".owl-stage .owl-item:last-child").hasClass("active");
  
  if (firstslide) {
    $(".arrows_prev").addClass("disabled");
  } else {    $(".arrows_prev").removeClass("disabled");
  }
  if (lastslide) {
    $(".arrows_next").addClass("disabled");
  } else {    $(".arrows_next").removeClass("disabled");
  }
}
/*** end of function***/
  
/*** owl initialize***/
  carousel.owlCarousel({
  touchDrag: true,
  loop: false,
  margin: 40,
  items: 3
});
DisableBtn(); 
$('.reviews__arrows .arrows_prev').click(function () {
  $(".reviews__carousel").trigger("prev.owl.carousel");
});
$('.reviews__arrows .arrows_next').click(function () {
  $(".reviews__carousel").trigger("next.owl.carousel");
});

/*** owl initialize***/  
carousel.on('translated.owl.carousel', function(event) {
  DisableBtn();
});  
});