How can I fix the gap under my porch inexpensively?

Sounds like the concrete is settling. I had a neighbor that did not want to put a lot of money into fixing a problem like this. They built "deck steps" and a covered the porch with deck as well. Solved the problem and looked nice "enough". Like your garden..

You can have the cement lifted but a professional has to do it. I don't think it's very expensive. there is also a cement caulk but that wouldn't look as good and it may keep sinking.

What about mortar with some inexpensive patio stone? It can go around the side of deck and in back of bottom step to cover gap.

There is a cement product that comes in a tube. You use it the like you would caulking. Carefully squeeze it in the separation and let dry. If the split is deep, I recommend doing one application...let it dry, then do another. Home Depot carries this product in the building supply section and I think Lowes does as well.

Pack a cheap filling in first then use your more expensive filling

I have the same problem and so I have allowed English ivy to grow across the gap between the porch and the sidewalk it looks very pretty and definitely hides the gap.

It.s not the landing that is shifting. It's the concrete walk that is sinking. Water is flowing from the garden bed towards, over and under the walk. You need to block/divert the water flow or the walk will continue to sink. You can fill the gap with a latex modified cement mix and smooth it out. It will fail if the problem isn't corrected.

The walkway is sinking, not the step. A concrete leveling company can "mud jack" the walk. Look in the yellow pages for "concrete leveling", and get it done professionally. They even level highways like this. It's not very expensive and it works. They drill a couple of holes in the walk and pump cement under the slab, then plug the holes. Done.

I agree with doing it right and get a mud jacker there to fix it. They can identify any other problem areas too