It is a mistake.

"Our end" (or "my end") refers to someone's side of an arrangement, procedure, or sometimes a point of view. You might hear:

From our end, things look fine

There is no problem at our end.

"On" our end could possibly be correct in a context where you would normally say the problem is "on" something - for example when there is interference on a telephone call, there is said to be a problem "on the line", so in such a situation you perhaps might say "there is a problem on my end (of the call/line)".

"In our end" seems the most unlikely to be used correctly, and certainly does not sound correct in the context of your example, which should be "at":

We are unable to locate your order at our end.

This is because it speaks about locating something, and you would use "at" to denote a location.

Answer from Astralbee on Stack Exchange
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Ludwig
ludwig.guru › s › on+their+end
on their end | Meaning, Grammar Guide & Usage Examples
The phrase 'on their end' is correct ... else is responsible for a certain action or process. For example: "We've done our part; it's up to the banks to finish the paperwork on their end." ... No one was hurt on their end. ... That way, startups only have one entity in the cap table, which ...
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TextRanch
textranch.com › 307176 › in-their-end › or › from-their-end
in their end or from their end?
This phrase is used to describe a situation or outcome as it relates to the individuals or group being discussed. ... In their end, the project was a success.
People also ask

What phrases are similar to "at their end"?
Similar phrases include ""on their part"", "from their perspective", or "in their case", each emphasizing a particular viewpoint or action.
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ludwig.guru
ludwig.guru › s › at+their+end
at their end | Meaning, Grammar Guide & Usage Examples | Ludwig.guru
What does "at their end" mean when referring to a process?
When referring to a process, "at their end" can signify the final stage or the responsibilities involved at the conclusion of that process, similar to saying "upon their completion".
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ludwig.guru
ludwig.guru › s › at+their+end
at their end | Meaning, Grammar Guide & Usage Examples | Ludwig.guru
How can I use "at their end" in a sentence?
Use "at their end" to refer to the conclusion, perspective, or responsibility of a specific group or entity. For example, "The company faced challenges "on their part" to meet deadlines."
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ludwig.guru
ludwig.guru › s › at+their+end
at their end | Meaning, Grammar Guide & Usage Examples | Ludwig.guru
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LanguageTool
languagetool.org › home › which is correct, “at the end” or “in the end”?
Which Is Correct, “At the End” or “In the End”?
June 17, 2025 - Remember that you can use at the end correctly if you use it the same way you would at the beginning. I was at the beginning of the line. I was at the end of the line. In the end is an idiomatic expression that can mean “ultimately,” “when everything is considered,” or “in conclusion.” ...
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Ludwig
ludwig.guru › s › at+their+end
at their end | Meaning, Grammar Guide & Usage Examples | Ludwig.guru
In summary, "at their end" serves as a prepositional phrase that indicates a concluding point, a specific viewpoint, or an area of responsibility for a group. Ludwig's analysis indicates that it is grammatically correct and frequently used across various contexts, including News & Media and Science.
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Dictionary.com
dictionary.com › e › their-vs-there-vs-theyre
“Their” vs. “There” vs. “They’re”: What’s the ...
October 24, 2024 - Many common adverbs end in -ly, like quickly, usually, and completely, but not all adverbs do. She is there now. There is also used as a pronoun introducing the subject of a sentence or clause: There is still hope. Their is the possessive case of the pronoun they, meaning belonging to them. As in: They left their cell phones at home. Their is generally plural, but it is increasingly accepted in place of the singular his or her after words such as someone:
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Ludwig
ludwig.guru › s › from+their+end
from their end | Meaning, Grammar Guide & Usage Examples
"from their end" is a correct and usable phrase in written English. It can be used to indicate that someone (the "their" in the phrase) is responsible for a certain action or outcome.
Find elsewhere
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Quora
quora.com › At-the-end-of-on-the-end-of-and-in-the-end-of-How-to-use-each-of-these
“At the end of”, “on the end of”, and “in the end of “ How to use each of these? - Quora
Answer (1 of 9): Use “on the end of” when you are speaking of an elongated surface, upon which something is standing, sitting, fastened etc. * “Joe is fishing on the end of the pier.” * “Sally had a ladybug on the end of her finger.” * “Tie this flag on the end of that pole.” Use "in the end ...
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Ginger Software
gingersoftware.com › english-online › spelling-book › confusing-words › their-there-theyre
Their vs. There vs. They're – The Correct Way to Use Each | Confusing Words
Their indicates ownership and has the word heir in its last four letters. An heir is someone who inherits something or will take ownership of something. There normally means ‘that place’ and has the word here in its last four letters, so we can think of it like in the sense of position – here and there.
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English Lessons Brighton
englishlessonsbrighton.co.uk › home › blog › “at the end” vs “in the end” explained with examples
"At the end" vs "in the end" explained with examples - English Lessons Brighton
February 18, 2021 - If the uses of these phrases aren’t ... difference between at and in in general. Simply put, at the end refers to a specific time or location, whilst in the end is an idiomatic phrase that means in conclusion or in summary....
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YourDictionary
yourdictionary.com › vocabulary › versus › meanings › rules for using there, their and they're
Rules for Using There, Their and They're | YourDictionary
November 18, 2020 - We jogged from way over there to the end of the block, then we sprinted the rest of the way home. The child took one look at the haunted house and shrieked, "I am never stepping foot in there!" My friend recently visited Ireland and loved it. I can’t wait to go there next year. The term there can also work as an adverb. In this sense, it is used to mean the opposite of the word “here.” ... The word there is sometimes used to modify a noun or pronoun, which means that it functions as an adjective.
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EnglishAlex
englishalex.com › post › in-the-end-vs-at-the-end-what-s-the-difference
"In the end" vs. "At the end": What's the difference?
March 26, 2022 - A single word can change the meaning and usage of a phrase. This is the case with "in the end" and "at the end." Let's look at the general differences between these phrases, and then look at them one at a time.
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Collins Dictionary
collinsdictionary.com › dictionary › english › end
END definition and meaning | Collins English Dictionary
[VERB adverb/preposition] Does responsibility end at the fitting of car seats? [VERB adverb/preposition] ... You can refer to someone's death as their end, especially when you are talking about the way that they died or might die.
Published   February 22, 2018
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Reddit
reddit.com › r/englishlearning › what is the difference between "at the end" with "in the end"?
r/EnglishLearning on Reddit: what is the difference between "at the end" with "in the end"?
July 12, 2022 - apparently, you use "in" only in the idiom "in the end" (meaning "finally"). In all other cases we should use "at": ... Typically I use "in the end" as a conclusion, summary or reflection of a story.
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Espresso English
espressoenglish.net › home › english tips blog › “in the end” or “at the end”?
"In the end" or "At the end"? - Espresso English
July 16, 2024 - We use “in the end” to mean “finally,” or “after a long time,” or “after everything is considered”: We had a lot of arguments, but in the end we came to an agreement.
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Encyclopedia Britannica
britannica.com › dictionary › end
End Definition & Meaning | Britannica Dictionary
b [+ object] : to stop or finish (something) : to cause (something) to no longer continue to happen or exist · They ended [=concluded] the meeting at noon. The allegations could end his career.
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Encyclopedia Britannica
britannica.com › dictionary › eb › qa › in-the-end-at-the-end
In the end / at the end | Britannica Dictionary
At the end is used in the idiom "at the end of the day." which means something similar to in the end (= when everything is considered). However, at the end is most commonly used more literally, as a prepositional phrase followed by of, to refer ...
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WordReference
forum.wordreference.com › english only › english only
The difference between an end and the end | WordReference Forums
December 9, 2018 - = The conversation reached one of its ends. As soon as I realize that there are more than one end I ask myself "What are the other ones?" How do we tell them one from another? I am pretty sure that in terms of time any end of a conversation is the same end. We came to the end of the conversation. Our conversation came to an end. So, in our physical world either we use "the end" or "an end" we get the same end unless we indicate the nature of such an end. I mean if we want a conversation to end in a certain way then I can see how "the end" can be used and it looks justified to me.