Browsing by Author "Rahman, Gauhar"
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Article Citation Count: Rashid, Saima...et al. (2020). "A New Dynamic Scheme via Fractional Operators on Time Scale", Frontiers in Physics, Vol. 8.A New Dynamic Scheme via Fractional Operators on Time Scale(2020) Rashid, Saima; Noor, Muhammad Aslam; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Rahman, Gauhar; 56389The 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.Article Citation Count: Rahman, G...et al. (2020). "Bounds of Generalized Proportional Fractional Integrals in General Form Via Convex Functions and Their Applications",Mathematics, Vol. 8, No. 1.Bounds of Generalized Proportional Fractional Integrals in General Form Via Convex Functions and Their Applications(MDPI AG, 2020) Rahman, Gauhar; Abdeljawad, Thabet; Jarad, Fahd; Nisar, Kottakkaran Sooppy; 234808In 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.Article Citation Count: Rahman, G...et al. (2019). "Certain Inequalities Via Generalized Proportional Hadamard Fractional Integral Operators",Advances in Difference Equations, Vol. 2019, No. 1.Certain Inequalities Via Generalized Proportional Hadamard Fractional Integral Operators(Springer International Publishing, 2019) Rahman, Gauhar; Abdeljawad, Thabet; Jarad, Fahd; Khan, Aftab; Nisar, Kottakkaran Sooppy; 234808In 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.Article Citation Count: Baleanu, Dumitru...et al. (2021). "Hermite-Hadamard-Fejer type inequalities via fractional integral of a function concerning another function", AIMS Mathematics, Vol. 6, No. 5, pp. 4280-4295.Hermite-Hadamard-Fejer type inequalities via fractional integral of a function concerning another function(2021) Baleanu, Dumitru; Samraiz, Muhammad; Perveen, Zahida; Iqbal, Sajid; Nisar, Kottakkaran Sooppy; Rahman, Gauhar; 56389In this paper, we at first develop a generalized integral identity by associating Riemann-Liouville (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. © 2021 the Author(s), licensee AIMS Press.Article Citation Count: Huang, Wen-Hua;...et.al. (2023). "Modified Atangana-Baleanu fractional operators involving generalized Mittag-Leffler function", Alexandria Engineering Journal, Vol.75, pp.639-648.Modified Atangana-Baleanu fractional operators involving generalized Mittag-Leffler function(2023) Huang, Wen-Hua; Samraiz, Muhammad; Mehmood, Ahsan; Baleanu, Dumitru; Rahman, Gauhar; Naheed, Saima; 56389In this paper, we are going to deal with fractional operators (FOs) with non-singular kernels 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 established. 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.Article Citation Count: Rahman, Gauhar...et al. (2021). "On the weighted fractional integral inequalities for Chebyshev functionals", Advances in Difference Equations, Vol. 2021, No. 1.On the weighted fractional integral inequalities for Chebyshev functionals(2021) Rahman, Gauhar; Nisar, Kottakkaran Sooppy; Khan, Sami Ullah; Baleanu, Dumitru; Vijayakumar, V.; 56389The 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 ω(θ) and G(θ) 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 ω(θ) and G(θ).Article Citation Count: Nisar, Kottakkaran Sooppy...et al. (2020). "On the weighted fractional Pólya–Szegö and Chebyshev-types integral inequalities concerning another function", Advances in Difference Equations, Vol. 2020, No. 1.On the weighted fractional Pólya–Szegö and Chebyshev-types integral inequalities concerning another function(2020) Nisar, Kottakkaran Sooppy; Rahman, Gauhar; Baleanu, Dumitru; Samraiz, Muhammad; Iqbal, Sajid; 56389The primary objective of this present paper is to establish certain new weighted fractional Pólya–Szegö and Chebyshev type integral inequalities by employing the generalized weighted fractional integral involving another function Ψ 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 ω(θ) and Ψ (θ). Also, the Pólya–Szegö 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 ω(θ) and Ψ (θ). Additionally, examples of constructing bounded functions are also presented in the paper.Article 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; 56389Integral 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.Article 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, MuhammadIn 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.
