Browsing by Author "Rahman, Gauhar"

Now showing 1 - 9 of 9

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: 12
Citation - Scopus: 15
On the Weighted Fractional Integral Inequalities for Chebyshev Functionals
(Springer, 2021) Nisar, Kottakkaran Sooppy; Khan, Sami Ullah; Baleanu, Dumitru; Vijayakumar, V.; Rahman, Gauhar
The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev's functionals by utilizing a fractional generalized weighted fractional integral involving another function G in the kernel. Also, we present weighted fractional integral inequalities for the weighted and extended Chebyshev's functionals. One can easily investigate some new inequalities involving all other type weighted fractional integrals associated with Chebyshev's functionals with certain choices of omega(theta) and G(theta) as discussed in the literature. Furthermore, the obtained weighted fractional integral inequalities will cover the inequalities for all other type fractional integrals such as Katugampola fractional integrals, generalized Riemann-Liouville fractional integrals, conformable fractional integrals and Hadamard fractional integrals associated with Chebyshev's functionals with certain choices of omega(theta) and G(theta).
Citation - WoS: 13
Citation - Scopus: 14
Hermite-Hadamard Type Inequalities Via Fractional Integral of a Function Concerning Another Function
(Amer inst Mathematical Sciences-aims, 2021) Samraiz, Muhammad; Perveen, Zahida; Iqbal, Sajid; Nisar, Kottakkaran Sooppy; Rahman, Gauhar; Baleanu, Dumitru
In this paper, we at first develop a generalized integral identity by associating RiemannLiouville (RL) fractional integral of a function concerning another function. By using this identity estimates for various convexities are accomplish which are fractional integral inequalities. From our results, we obtained bounds of known fractional results which are discussed in detail. As applications of the derived results, we obtain the mid-point-type inequalities. These outcomes might be helpful in the investigation of the uniqueness of partial differential equations and fractional boundary value problems.
Citation - WoS: 20
Citation - Scopus: 25
Modified Atangana-Baleanu Fractional Operators Involving Generalized Mittag-Leffler Function
(Elsevier, 2023) Samraiz, Muhammad; Mehmood, Ahsan; Baleanu, Dumitru; Rahman, Gauhar; Naheed, Saima; Huang, Wen-Hua
In this paper, we are going to deal with fractional operators (FOs) with non-singular ker-nels which is not an easy task because of its restriction at the origin. In this work, we first show the boundedness of the extended form of the modified Atangana-Baleanu (A-B) Caputo fractional derivative operator. The generalized Laplace transform is evaluated for the introduced operator. By using the generalized Laplace transform, we solve some fractional differential equations. The corresponding form of the Atangana-Baleanu Caputo fractional integral operator is also estab-lished. This integral operator is proved bounded and obtained its Laplace transform. The existence and Hyers-Ulam stability is explored. In the last results, we studied the relation between our defined operators. The operators in the literature are obtained as special cases for these newly explored FOs.& COPY; 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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.
Citation - WoS: 10
Citation - Scopus: 19
A New Dynamic Scheme Via Fractional Operators on Time Scale
(Frontiers Media Sa, 2020) Noor, Muhammad Aslam; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Rahman, Gauhar; Rashid, Saima
The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Gruss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics.
Citation - WoS: 31
Citation - Scopus: 32
Bounds of Generalized Proportional Fractional Integrals in General Form Via Convex Functions and Their Applications
(Mdpi, 2020) Jarad, Fahd; Nisar, Kottakkaran Sooppy; Rahman, Gauhar; Abdeljawad, Thabet
In this paper, our objective is to apply a new approach to establish bounds of sums of left and right proportional fractional integrals of a general type and obtain some related inequalities. From the obtained results, we deduce some new inequalities for classical generalized proportional fractional integrals as corollaries. These inequalities have a connection with some known and existing inequalities which are mentioned in the literature. In addition, some applications of the main results are presented.
Citation - WoS: 9
Citation - Scopus: 13
On the Weighted Fractional Polya-Szego and Chebyshev-Types Integral Inequalities Concerning Another Function
(Springer, 2020) Rahman, Gauhar; Baleanu, Dumitru; Samraiz, Muhammad; Iqbal, Sajid; Nisar, Kottakkaran Sooppy
The primary objective of this present paper is to establish certain new weighted fractional Polya-Szego and Chebyshev type integral inequalities by employing the generalized weighted fractional integral involving another function psi in the kernel. The inequalities presented in this paper cover some new inequalities involving all other type weighted fractional integrals by applying certain conditions on omega(theta) and psi (theta). Also, the Polya-Szego and Chebyshev type integral inequalities for all other type fractional integrals, such as the Katugampola fractional integrals, generalized Riemann-Liouville fractional integral, conformable fractional integral, and Hadamard fractional integral, are the special cases of our main results with certain choices of omega(theta) and psi(theta). Additionally, examples of constructing bounded functions are also presented in the paper.
Citation - WoS: 68
Citation - Scopus: 65
Certain Inequalities Via Generalized Proportional Hadamard Fractional Integral Operators
(Springer, 2019) Jarad, Fahd; Khan, Aftab; Nisar, Kottakkaran Sooppy; Rahman, Gauhar; Abdeljawad, Thabet
In the article, we introduce the generalized proportional Hadamard fractional integrals and establish several inequalities for convex functions in the framework of the defined class of fractional integrals. The given results are generalizations of some known results.