Browsing by Author "Mubeen, Shahid"

Now showing 1 - 2 of 2

Citation - WoS: 88
The Extended Mittag-Leffler Function Via Fractional Calculus
(int Scientific Research Publications, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa; Purohit, Sunil Dutt; Mubeen, Shahid; Arshad, Muhammad; Rahman, Gauhar
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. (C) 2017 All rights reserved.
Citation - WoS: 5
Citation - Scopus: 8
Some Generalized Fractional Integral Inequalities With Nonsingular Function as a Kernel
(Amer inst Mathematical Sciences-aims, 2021) Ali, Rana Safdar; Nayab, Iqra; Rahman, Gauhar; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Mubeen, Shahid
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.