Rahman, GauharBaleanu, DumitruAl Qurashi, Maysaa MohamedPurohit, Sunil DuttMubeen, ShahidArshad, Muhammad2020-02-282020-02-282017Rahman, Gauhar...et al. (2017). "The extended Mittag-Leffler function via fractional calculus", Journal Of Nonlinear Sciences And Applications, Vol.10, No.8, pp.4244-4253.2008-1898http://hdl.handle.net/20.500.12416/2550In this study, our main attempt is to introduce fractional calculus (fractional integral and differential) operators which contain the following new family of extended Mittag-Leffler function: E-alpha,beta(gamma;q,c) (z) = Sigma(infinity)(n=0) B-p (gamma + nq, c - gamma)(c)(nq) z(n)/B(gamma, c - gamma)Gamma(alpha n + beta) n!' (z,beta,gamma is an element of C), as its kernel. We also investigate a certain number of their consequences containing the said function in their kernels.eninfo:eu-repo/semantics/closedAccessFractional IntegrationDifferential OperatorMittag-Leffler FunctionLebesgue Measurable FunctionExtended Mittag-Leffler FunctionArticle1084244425310.22436/jnsa.010.08.19