Abdeljawad, ThabetBaleanu, Dumitru2017-01-232025-09-182017-01-232025-09-182011Abdeljawad, T., Baleanu, D. (2011). Caputo q-fractional initial value problems and a q-analogue Mittag-Leffler function. Communications In Nonlinear Science And Numerical Simulation, 16(12), 4682-4688. http://dx.doi.org/10.1088/10.1016/j.cnsns.2011.01.0261007-57041878-7274https://doi.org/10.1016/j.cnsns.2011.01.026https://hdl.handle.net/20.500.12416/14913Abdeljawad, Thabet/0000-0002-8889-3768Caputo 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.eninfo:eu-repo/semantics/openAccessLeft Q-Fractional IntegralRight Q-Fractional IntegralCaputo Left And Right Q-Fractional DerivativesQ-OperatorQ-Mittag-Leffler FunctionTime ScaleArticle10.1016/j.cnsns.2011.01.0262-s2.0-79960269969