Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 16, Issue 12, Pages 4682-4688Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2011.01.026
Keywords
Left q-fractional integral; Right q-fractional integral; Caputo left and right q-fractional derivatives; Q-operator; q-Mittag-Leffler function; Time scale
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Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about q-fractional integrals are proposed as well. (C) 2011 Elsevier B.V. All rights reserved.
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