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Study of new class of q-fractional derivative and its properties (1905.11115v2)
Published 27 May 2019 in math.GM
Abstract: There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related to this operator and some properties of this operator as boundness are investigated. Moreover, related q-difference equation is discussed and in the aid of q-successive approximation , existence and uniqueness are studied.