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It is proper to use "," between A and B

A, B are the objects that are part of the equation.

instead of "and"

A and B are the objects that are part of the equation.

in formal academic writing?

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It is understandable, but not really recommended, unless you are very short of space. It looks very "clipped". It looks like you are trying to use the very fewest number of words, and it makes the text flow less well.

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    For example, we wouldn't say that "A zebra is black, white"; we'd say "A zebra is black and white". When there are more items in a list, we say "The cat is black, white and orange" (with optional comma after "white" depending on your style guide and locale).
    – Nigel Touch
    Oct 28, 2021 at 9:54
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    Using a comma instead of "and" is common practice in headlinese. In just about every other context I would call it simply wrong.
    – randomhead
    Oct 28, 2021 at 14:01
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In formal mathematics it is appropriate to write, for example

Let A, B be sets, and let C be their intersection.

It is not appropriate in most other contexts.

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In formal academic writing, you must not replace "and" with a "," in sentences similar to yours. This is absolutely wrong. Look up a guide like the Chicago Manual of Style or the APA, and find out what they say about "commas" and their usage.

But you can (or should) when you are dealing with coordinate adjectives:

We walked down the long, narrow path.

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