If by "concept" you simply mean that you were inspired by these libraries, but did not use any actual code from them, then your code may not be a derivative of either of them in the first place. If this is the case, then you have no obligations, although it would be polite to put links to those libraries in your README.md or some other place where users will see them. This is because abstract ideas and concepts are not subject to copyright protection in most countries. See for example 17 USC 102(b).
On the other hand, if "concept" refers to a C++
concept (or the same in another language), or if you have actually copied (and/or modified) code from both libraries, then you must include the text of both licenses, and in the case of Apache you must specifically indicate that you have changed the original. If the Apache library has a file called "NOTICE" or something similar, you must include a verbatim copy of that file, either in a similar file (in the case of source distributions), or in the documentation and other ancillary materials that are provided along with binaries.
In either case, you may license the resulting software under whatever license you choose. Neither Apache nor BSD3 is a copyleft license. If you choose to use a third license, then your own LICENSE or COPYING file should clearly indicate that the Apache and BSD3 license texts apply to the upstream distribution, and not to your library. If you want your library to be maximally "polite," it would be good practice to dual-license your library under both Apache and BSD3, so that the upstream projects can take your code and use it freely, but you are not required to do this if you do not wish to. To do this, it is enough to simply add a notice at the top of the LICENSE file saying something like "This library is available under both the Apache and the BSD license, as shown below. You may select the license of your choice." You would then include the text of both licenses, perhaps with a separator.