All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
In order to determine whether an act is an innovation or not, we should review the restrictions and criteria that scholars have established. Ash-Shaatibi who followed the school of Maalik defined it as, “An invented way in religion that is similar to the Sharee‘ah-approved way, but in reality it contradicts it. Usually it is intended for exaggerating in worshipping Allaah The Almighty.”
Ash-Shaatibi gave an example of certain forms of innovation such as mentioning Allaah The Almighty in congregation in a loud voice and celebrating the birthday of the Prophet, sallaallaahu ‘alayhi wa sallam . Also, consistently performing certain acts of worship at certain times that were not specified in the religion such as fasting on the fifteenth of Sha‘baan and spending the night before it in prayer and worship.
Another criterion that was identified by scholars is that anything that was not done by the Prophet, sallaallaahu ‘alayhi wa sallam, while its cause was available and there was no hindrance, is an innovation.
Ask yourself why you specifically chose Thursday for reciting Chapter Al-Kahf. This was not narrated as being from the actions of the Prophet, sallaallaahu ‘alayhi wa sallam. Therefore, the problem is that this was not mentioned in Sharee‘ah!
In conclusion, it is not permissible to specify Thursday for reciting this chapter as this is an innovation. However, it is permissible to read this chapter or any other one without specifying a certain time.
It was narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said that any one who reads Chapter Al-Kahf on Friday would have light the distance between him and the Sacred Masjid (in Makkah) and that this would last until the following Friday. [Al-Haakim, Al-Bayhaqi, Al-Albaani: Authenticated]
Thus, reciting Chapter Al-Kahf every Friday is a Sunnah and it can be read individually or in a group. Imaam Ash-Shaafi‘i said that it is favorable to recite Chapter Al-Kahf at that time. There were some narrations that said so but they were not authenticated. Consequently, it is a Sunnah to recite Chapter Al-Kahf constantly only on Fridays.
Allaah Knows best.