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q-FRACTIONAL INITIAL VALUE PROBLEMS AND q-ANALOGUE OF GENERALIZED MITTAG-LEFFLER FUNCTIONKeywords: Left q-fractional integral , right q-fractional integral , Caputo left and right q-fractional derivatives , generalized Mittag-Leffler function. Abstract: In the present paper, the author introduced q-analogues of generalized Mittag-Leffler function referred by Prabhakar [23]. Results derived in this paper are the extensions of the results derived earlier by Abdeljawad et al. [19]. Some special cases of interest are also discussed.
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