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This paper is devoted to fractional q-derivative of special functions. To begin with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit [8] and Sharma and Jain [9]. As a special case, of fractional q-differentiation of J-Function has been obtained.

In this paper we establish a relation Dirichlet average of J-Function, using fractional derivative.