Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 49Citation - Scopus: 64New Estimates Considering the Generalized Proportional Hadamard Fractional Integral Operators(Springer, 2020) Rashid, Saima; Jarad, Fahd; Kalsoom, Humaira; Chu, Yu-Ming; Zhou, Shuang-ShuangIn the article, we describe the Gruss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators.Article Citation - WoS: 9Citation - Scopus: 10More Efficient Estimates Via H-Discrete Fractional Calculus Theory and Applications(Pergamon-elsevier Science Ltd, 2021) Sultana, Sobia; Jarad, Fahd; Jafari, Hossein; Hamed, Y. S.; Rashid, SaimaDiscrete fractional calculus (DFC) is continuously spreading in the engineering practice, neural networks, chaotic maps, and image encryption, which is appropriately assumed for discrete-time modelling in continuum problems. First, we start with a novel discrete h-proportional fractional sum defined on the time scale hZ so as to give the premise to the more broad and complex structures, for example, the suitably accustomed transformations conjuring the property of observing the new chaotic behaviors of the logistic map. Here, we aim to present the novel discrete versions of Gruss and certain other associated variants by employing discrete h-proportional fractional sums are established. Moreover, several novel consequences are recaptured by the h-discrete fractional sums. The present study deals with the modification of Young, weighted-arithmetic and geometric mean formula by taking into account changes in the exponential function in the kernel represented by the parameters of the operator, varying delivery noted outcomes. In addition, two illustrative examples are apprehended to demonstrate the applicability and efficiency of the proposed technique. (C) 2021 Elsevier Ltd. All rights reserved.Article Citation - WoS: 85Citation - Scopus: 108Inequalities by Means of Generalized Proportional Fractional Integral Operators With Respect To Another Function(Mdpi, 2019) Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu-Ming; Rashid, SaimaIn this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Psi. The authors prove several inequalities for newly defined GPF-integral with respect to another function Psi. Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Psi and the proportionality index sigma. Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.Article Citation - WoS: 25Citation - Scopus: 37On Gruss Inequalities Within Generalized K-Fractional Integrals(Springer, 2020) Noor, Muhammad Aslam; Noor, Khalida Inayat; Baleanu, Dumitru; Liu, Jia-Bao; Rashid, Saima; Jarad, FahdIn this paper, we introduce the generalized K-fractional integral in the frame of a new parameter K > 0. This paper offers some new important inequalities of Gruss type using the generalized K-fractional integral and associated integral inequalities. Our results with this new integral operator have the abilities to be implemented for the evaluation of many mathematical problems related to the real world applications.Article Citation - WoS: 10Citation - Scopus: 19A 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; Aslam Noor, MuhammadThe 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.