Browsing by Author "Khan, Zareen A."

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Citation Count: Khan, Zareen A...et al. (2020). "Derivation of dynamical integral inequalities based on two-dimensional time scales theory", Journal of Inequalities and Applications, Vol. 2020, No. 1.
Derivation of dynamical integral inequalities based on two-dimensional time scales theory
(2020) Khan, Zareen A.; Jarad, Fahd; Khan, Aziz; Khan, Hasib; 234808
The main goal of this paper is to set up some new estimates of a specific class of dynamic integral inequalities (DII) which are partially linear on a time scale T with two independent variables. These, from the one hand, sum up and, on the other hand, offer a helpful method for both the qualitative and quantitative study of dynamic equations on time scales. Some applications are taken into consideration to show the validity of the fundamental results.
Citation Count: Khan, Zareen A...et al. (2020). "Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property", Advances in Difference Equations, Vol. 2020, No. 1.
Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property
(2020) Khan, Zareen A.; Rashid, Saima; Ashraf, Rehana; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In the paper, we extend some previous results dealing with the Hermite–Hadamard inequalities with fractal sets and several auxiliary results that vary with local fractional derivatives introduced in the recent literature. We provide new generalizations for the third-order differentiability by employing the local fractional technique for functions whose local fractional derivatives in the absolute values are generalized convex and obtain several bounds and new results applicable to convex functions by using the generalized Hölder and power-mean inequalities. As an application, numerous novel cases can be obtained from our outcomes. To ensure the feasibility of the proposed method, we present two examples to verify the method. It should be pointed out that the investigation of our findings in fractal analysis and inequality theory is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena. © 2020, The Author(s).
Citation Count: Khan, Zareen A...at all (2021). "Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications", Advances in Difference Equations, Vol. 2021, No. 1.
Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications
(2021) Khan, Zareen A.; Jarad, Fahd; Khan, Aziz; Khan, Hasib; 234808
By means of ς fractional sum operator, certain discrete fractional nonlinear inequalities are replicated in this text. Considering the methodology of discrete fractional calculus, we establish estimations of Gronwall type inequalities for unknown functions. These inequalities are of a new form comparative with the current writing discoveries up until this point and can be viewed as a supportive strategy to assess the solutions of discrete partial differential equations numerically. We show a couple of employments of the compensated inequalities to reflect the benefits of our work. The main outcomes might be demonstrated by the use of the examination procedure and the approach of the mean value hypothesis. © 2021, The Author(s).
Citation Count: Gul, Rozi...et al. (2021). "On a class of boundary value problems under ABC fractional derivative", Advances in Difference Equations, Vol. 2021, No. 1.
On a class of boundary value problems under ABC fractional derivative
(2021) Gul, Rozi; Shah, Kamal; Khan, Zareen A.; Jarad, Fahd; 234808
In this work, we establish some necessary results about existence theory to a class of boundary value problems (BVPs) of hybrid fractional differential equations (HFDEs) in the frame of Atangana–Baleanu–Caputo (ABC) fractional derivative. Making use of Krasnoselskii and Banach theorems, we obtain the required conditions. Some appropriate results of Hyers–Ulam (H–U) stability corresponding to the considered problem are also established. Also a pertinent example is given to demonstrate the results. © 2021, The Author(s).