Mathematics Subject Classification: 33D60, 33D90, 26A33Fractional q-integral operators of generalized Weyl type, involving generalized basic hypergeometric functions and a basic analogue of Fox’s H-function have been investigated. A number of integrals involving various q-functions have been evaluated as applications of the main results.
Mathematics Subject Classification: 33D60, 33E12, 26A33Based on the fractional q–integral with the parametric lower limit of integration, we consider the fractional q–derivative of Caputo type. Especially, its applications to q-exponential functions allow us to introduce q–analogues of the Mittag–Leffler function. Vice versa, those functions can be used for defining generalized operators in fractional q–calculus.
Mathematics Subject Classification: 33D15, 44A10, 44A20The present paper deals with the evaluation of the q-Laplace transforms of a product of basic analogues of the Bessel functions. As applications, several useful special cases have been deduced.
2000 Mathematics Subject Classification: 33D60, 26A33, 33C60The present paper envisages the applications of Riemann-Liouville fractional q-integral operator to a basic analogue of Fox H-function. Results involving the basic hypergeometric functions like Gq(.), Jv(x; q), Yv(x; q),Kv(x; q), Hv(x; q) and various other q-elementary functions associated with the Riemann-Liouville fractional q-integral operator have been deduced as special cases of the main result.