Browsing by Author "Mubeen, Shahid"

Now showing 1 - 2 of 2

Citation Count: Mubeen, Shahid...et al. (2021). "Some generalized fractional integral inequalities with nonsingular function as a kernel", AIMS MATHEMATICS, Vol. 6, No. 4, pp. 3352-337.
Some generalized fractional integral inequalities with nonsingular function as a kernel
(2021) Mubeen, Shahid; Ali, Rana Safdar; Nayab, Iqra; Rahman, Gauhar; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
Integral inequalities play a key role in applied and theoretical mathematics. The purpose of inequalities is to develop mathematical techniques in analysis. The goal of this paper is to develop a fractional integral operator having a non-singular function (generalized multi-index Bessel function) as a kernel and then to obtain some significant inequalities like Hermit Hadamard Mercer inequality, exponentially (s - m)-preinvex inequalities, Polya-Szego and Chebyshev type integral inequalities with the newly developed fractional operator. These results describe in general behave and provide the extension of fractional operator theory (FOT) in inequalities.
Citation Count: Rahman, 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.
The extended Mittag-Leffler function via fractional calculus
(Int Scientific Research Publications, 2017) Rahman, Gauhar; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Purohit, Sunil Dutt; Mubeen, Shahid; Arshad, Muhammad
In 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.