Browsing by Author "Noor, Muhammad Aslam"

Now showing 1 - 9 of 9

Citation - WoS: 10
Citation - Scopus: 18
A New Dynamic Scheme via Fractional Operators on Time Scale
(Frontiers Media Sa, 2020) Rashid, Saima; Baleanu, Dumitru; Noor, Muhammad Aslam; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Rahman, Gauhar; 56389; Matematik
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: 14
Citation - Scopus: 18
Grüss-type integrals inequalities via generalized proportional fractional operators
(Springer-verlag Italia Srl, 2020) Rashid, Saima; Jarad, Fahd; Jarad, Fahd; Noor, Muhammad Aslam; 234808; Matematik
In the article, we deal with the generalized proportional fractional integral, establish several kinds of inequalities such as Gruss-type and certain other inequalities by use of generalized proportional fractional integral. Moreover, several special cases are discussed. Also, we derive certain particular results by utilizing the connection between generalized proportional fractional integral and Riemann-Liouville integral. Furthermore, an illustrative example is presented to support our outcomes.
Citation - WoS: 84
Citation - Scopus: 105
Inequalities by means of generalized proportional fractional integral operators with respect to another function
(Mdpi, 2019) Rashid, Saima; Jarad, Fahd; Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu-Ming; 234808; Matematik
In 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.
Citation - WoS: 12
Citation - Scopus: 12
More new results on integral inequalities for generalized K-fractional conformable integral operators
(Amer inst Mathematical Sciences-aims, 2021) Chu, Yu-Ming; Jarad, Fahd; Rashid, Saima; Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; 234808; Matematik
This paper aims to investigate the several generalizations by newly proposed generalized K-fractional conformable integral operator. Based on these novel ideas, we derived a novel framework to study for Cebysev and Polya-Szego type inequalities by generalized K-fractional conformable integral operator. Several special cases are apprehended in the light of generalized fractional conformable integral. This novel strategy captures several existing results in the relative literature. We also aim at showing important connections of the results here with those including Riemann-Liouville fractional integral operator.
Citation - WoS: 25
Citation - Scopus: 35
On Gruss inequalities within generalized K-fractional integrals
(Springer, 2020) Jarad, Fahd; Rashid, Saima; Jarad, Fahd; Baleanu, Dumitru; Noor, Muhammad Aslam; Noor, Khalida Inayat; Baleanu, Dumitru; Liu, Jia-Bao; 56389; 234808; Matematik
In 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.
Citation - WoS: 2
On Polya-Szego Type Inequalities via K-Fractional Conformable Integrals
(Univ Punjab, dept Mathematics, 2020) Rashid, Saima; Jarad, Fahd; Jarad, Fahd; Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat; 234808; Matematik
The studies of inequalities regarding the fractional differential and integral operators are considered to be essential because of their potential applications among researchers. This paper consigns to the generalizations of novel fractional integral inequalities. The Polya-Szego type variants are generalized by involving K-fractional conformable integrals (KFCI): This is the K-analogue of the fractional conformable integrals. We discuss the implications and other consequences of the K-fractional conformable fractional integrals.
Citation - WoS: 41
Simpson's type integral inequalities for kappa-fractional integrals and their applications
(Amer inst Mathematical Sciences-aims, 2019) Rashid, Saima; Jarad, Fahd; Akdemir, Ahmet Ocak; Jarad, Fahd; Noor, Muhammad Aslam; Noor, Khalida Inayat; 234808; Matematik
In this paper, some new inequalities of Simpson's type are set up for the classes of functions whose derivatives of absolute are preinvex by means of kappa-fractional integrals. Additionally, by extraordinary choices of n and kappa, we give some diminished outcomes. Meanwhile, we also provide the inequalities for F-divergence measures and in probabilistic versions.
Citation - WoS: 38
Citation - Scopus: 54
Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications
(Mdpi, 2019) Abdeljawad, Thabet; Rashid, Saima; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Noor, Muhammad Aslam; 234808; Matematik
In the present paper, we investigate some Hermite-Hadamard (HH) inequalities related to generalized Riemann-Liouville fractional integral (GRLFI) via exponentially convex functions. We also show the fundamental identity for GRLFI having the first order derivative of a given exponentially convex function. Monotonicity and exponentially convexity of functions are used with some traditional and forthright inequalities. In the application part, we give examples and new inequalities for the special means.
Citation - WoS: 27
Citation - Scopus: 27
Some New Fractional Estimates of Inequalities for LR-p-Convex Interval-Valued Functions by Means of Pseudo Order Relation
(Mdpi, 2021) Khan, Muhammad Bilal; Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Noor, Muhammad Aslam; Baleanu, Dumitru; Garcia Guirao, Juan Luis; 56389; Matematik
It is a familiar fact that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis, both the inclusion relation (subset of) and pseudo order relation (<= p) are two different concepts. In this article, by using pseudo order relation, we introduce the new class of nonconvex functions known as LR-p-convex interval-valued functions (LR-p-convex-IVFs). With the help of this relation, we establish a strong relationship between LR-p-convex-IVFs and Hermite-Hadamard type inequalities (HH-type inequalities) via Katugampola fractional integral operator. Moreover, we have shown that our results include a wide class of new and known inequalities for LR-p-convex-IVFs and their variant forms as special cases. Useful examples that demonstrate the applicability of the theory proposed in this study are given. The concepts and techniques of this paper may be a starting point for further research in this area.