Try experimenting with the Blur Gallery filters in Photoshop - there are several kinds to choose from, such as Tilt Shift, Irish Blur, Path Blur etc.
The examples below began as a simple wave shape over a black background
Here's an example using the Iris Blur tool
You can go crazy with the Path Blur tool
It's possible to set up your InDesign document so the back and front page are shown as a spread instead of being two separate pages.
When creating the document, set it up with the wanted Number of Pages, enable Facing Pages and set Start Page # to 2.
Now your document only consists of whole spreads:
But the page numbers are wrong which will give you ...
Imagine your cover to be spread out, with the spine face up.
On your front page 'spread', draw one big shape that extends to the left of the front cover far enough to cover the imaginary back cover as well, including bleed. Fill this shape with your desired gradient.
Copy this object.
On your back cover 'spread', choose Edit > Paste in Place (Ctrl/Cmd+Alt+...
Apparently this artwork is called Rimova and was made by Nicholas Law. Most of his art seems to have the same look so I'm sure that he has spent a lot of time refining this technique. A similar result is probably more than a few clicks away.
Obviously I can't tell you exactly how this was made, but I'll try to give you some inspiration for further ...
Since you've added "Photo-editing" as the tag I'll attempt an answer, but you can forget Illustrator. It's no good for editing photos which are raster images.
It's pretty easy to create similar effects in Photoshop, or other similar raster image editors.
In Photoshop you could take a regular photo, turn it into a Smart Object, then apply an Iris Blur to it,...
If you want to tinker you can try Illustrator's Blending:
The next cartoon shows how the arc is made:
Start with the edge curves
Make a three step blend to get 3 intermediate curves, expand the blend and ungroup the parts
Convert the strokes to outlines to be able to make width variations with the direct selection tool. You can as well use path width tool, ...
Simply use a thick stroke as opposed to a shape, and apply a gradient to the stroke.
You can expand the gradient stroke afterwards, resulting in a gradient mesh object.
You can also stack multiple strokes via the Appearance Panel to add additional gradients. Here I've added a second stroke with a gradient to indicate shadowing on the lower portion...
You will need to group the object, but the gradient tool for some reason does not allow you to apply a gradient to a grouped object directly (as you can see me demonstrate in the middle of the attached GIF). I'm not sure if this is a bug or not - but there is a workaround!
Group the text and the object, then add a new fill from the appearance panel.
There could be different ways to achieve this, but here's one way:
Convert text to outlines via Type → Create Outlines. Keep an editable copy if you need to.
Select all, including bullseye and apply gradient. This will apply a gradient to each individual letter and shape.
Hit G and drag your mouse around around, see what happens.
Take it from there and ...