The rising generation

"Rising generation" is a nonbiblical Book of Mormon term. 

there were many of the rising generation that could not understand the words of king Benjamin

(Mosiah 26:1)

I say unto you the aged, and also the middle aged, and the rising generation; yea, to cry unto them that they must repent and be born again.

(Alma 5:49)

And thus were the Lamanites afflicted also, and began to decrease as to their faith and righteousness, because of the wickedness of the rising generation.

(3 Nephi 1:30)

And also it is an imperative duty that we owe to all the rising generation, and to all the pure in heart—

(Doctrine and Covenants 123:11)

8 Preaching and expounding, writing, copying, selecting, and obtaining all things which shall be for the good of the church, and for the rising generations that shall grow up on the land of Zion, to possess it from generation to generation, forever and ever. Amen.

(Doctrine and Covenants 69:8)

Here are examples of how Jonathan Edwards used the term.

http://edwards.yale.edu/archive?____pgfa=aHR0cDovL2Vkd2FyZHMueWFsZS5lZHUvY2dpLWJpbi9uZXdwaGlsby9zZWFyY2gzdA&dbname=wjeo&word=Rising+generation+

1. I beseech you, brethren, seasonably to consider how dark the cloud is that hangs over you, and how melancholy the prospect (especially with regard to the rising generation) in many respects. I have long been intimately acquainted with your religious circumstances, your notions and principles, your advantages and dangers; having had perhaps greater opportunity for it than any other person on earth. Before I left you, it was very evident, that Arminianism, and other loose notions in religion, and Mr. Taylor's in particular, began to get some footing among you; and there were some things special in your circumstances, that threatened a great prevailing of such like notions: which if they should by degrees generally prevail, will doubtless by degrees put an end to what used to be called saving religion.

NOTE: Joseph Smith wrote in his 1832 history that

At about the age of twelve years my mind become seriously imprest with regard to the all importent concerns of for the wellfare of my immortal Soul which led me to searching the scriptures believeing as I was taught, that they contained the word of God thus applying myself to them and my intimate acquaintance with those of differant denominations led me to marvel excedingly

https://www.josephsmithpapers.org/paper-summary/history-circa-summer-1832/2