Kober fractional q-derivative operators

Abstract

In the present paper, we define right and left sided Kober fractional q-derivative operators and show that these derivative operators are left inverse operators of Kober fractional q-integral operators. We obtain the images of generalized basic hypergeometric function and basic analogue of the H-function under these operators. We also deduce several interesting results involving q-analogues of some classical functions as special cases of our main findings.

Keywords

• Kober fractional q-integral operator
• Kober fractional q-derivative operator
• generalized basic hypergeometric function
• basic analogue of Fox H-function
• basic analogue of Bessel function