This is my best educated guess. I am not a legal expert.

The expression ولاية قضائية refers to the authority invested in a court over a specific type of cases. In English, this is referred to as "jurisdiction." For example, a civilian court does not have jurisdiction over cases involving military personnel, and vice versa.

The expression الإلغاء refers to a court action to repeal or revoke administrative rules or procedures. One can file a lawsuit requesting to have certain administrative procedures repealed. This only applies to administrative procedures, not laws. Laws can only be reversed by the legislature or by a constitutional court declaring the said laws as unconstitutional. The process of examining administrative procedures and adjudicating their repeal when challenged is referred to as "judicial review." The term "review" implies the possibility of revocation if the court deems revocation appropriate.

The expression التعويض refers to a judgment by the court to pay money to a claimant who has unfairly suffered due to a particular set of administrative procedures. The award given to the injured party is referred to as "damages" in legal language.

You can google the terms "jurisdiction," "judicial review," and "damages" to find out more about these concepts and how they are expressed in English.

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Note added at 4 hrs (2020-05-30 17:45:40 GMT)
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You can also read more about الإلغاء والتعويض here:

https://www.aleqt.com/2011/01/09/article_489089.html

You can find out much more if you google these two terms together.

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Note added at 4 hrs (2020-05-30 18:35:01 GMT)
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To read about the process of judicial review of administrative actions or procedures, you can take a look at this page:

https://lawshelf.com/videocoursesmoduleview/judicial-review-...

Please note that the process of judicial review, including jurisdictional considerations, vary from country to country, but the concept is the same.

Also, please note that in some Arab countries, "jurisdiction" is called اختصاص.

Administrative Circuit............, which has abatement and damages ruling jurisdiction.