Переместите скрипт jQuery в начало всех скриптов, проверьте фрагмент
var $ = jQuery;
$('#carouselExampleSlidesOnly').carousel({
interval: 2000
})
.carousel-inner {
background-image: url("https://worldtransfer.online/wp-content/uploads/2016/09/worldmap-bg.jpg");
background-position: center center;
background-repeat: no-repeat;
background-size: cover;
height: 250px
}
.carousel-caption {
top: 1em;
}
.carousel {
position: relative
}
.d_flex {
position: absolute;
z-index: 99;
justify-content: center;
top: 10%;
text-align: center;
align-items: center;
width: 100%;
}
.carousel-text {
position: absolute;
z-index: 99;
height:100%;
top:100%
}
<script src="https://code.jquery.com/jquery-3.2.1.slim.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/js/bootstrap.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.12.9/umd/popper.min.js"></script>
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css" rel="stylesheet" />
<div id="carouselExampleSlidesOnly" class="carousel slide" data-ride="carousel">
<div class="d_flex d-flex">
<h2 class="text-uppercase text-white">We Architect,</h2>
<h3 class="text-white">Design and Develop</h3>
</div>
<div class="carousel-inner">
<div class="carousel-item active">
<div class="carousel-caption" >
<div class="carousel-text">
<h1 class="text-uppercase">
<span class="text-warning pr-3">Web</span>Application
</h1>
</div>
</div>
</div>
<div class="carousel-item">
<div class="carousel-caption">
<div class="carousel-text">
<h1 class="text-uppercase">
<span class="text-warning pr-3">Mobile</span>Application
</h1>
</div>
</div>
</div>
<div class="carousel-item">
<div class="carousel-caption" >
<div class="carousel-text">
<h1 class="text-uppercase">
<span class="text-warning pr-3">Desktop</span>Application
</h1>
</div>
</div>
</div>
</div>
</div>