Abstract
We first study Katugampola fractional q-integral and q-derivative in the space L1qp [a, b] and obtain some properties of these operators, which include the image of power function, semi group property and composition of these operators. Next, we look at the existence and uniqueness of solution to generalized fractional q-Cauchy type problems involving Katugampola fractional q-derivative. Also, we obtain their compact form solutions using Adomian decomposition method, in terms of q-Mittag-Leffler type functions.
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