The aim of this paper is to give an alternative solution for the $q$-kinetic equation involving the Riemann--Liouville fractional $q$-integral operator. The solution is obtained in terms of the $q$-Mittag--Leffler functions using inverse $q$-Sumudu transform. As applications, some corollaries are presented to illustrate the main results.
PUROHIT, SUNIL DUTT and UÇAR, FARUK
"An application of $q$-Sumudu transform for fractional $q$-kinetic equation,"
Turkish Journal of Mathematics: Vol. 42:
2, Article 25.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss2/25