Simpson’s type inequalities for η-convex functions via k-Riemann–Liouville fractional integrals

We introduce some Simpson's type integral inequalities via k-Riemann–Liouville fractional integrals for functions whose derivatives are η-convex. These results generalize some results in the literature

Generalized weighted Ostrowski and Ostrowski-Gruss type inequalities on time scales via a parameter function

We prove generalized weighted Ostrowski and Ostrowski–Gr ¨uss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and Barnett. Furthermore, we apply our results to the continuous, discrete, and quantum cases, to obtain some interesting new inequalitie

Time Scale Inequalities of the Ostrowski Type for Functions Differentiable on the Coordinates

In 2016, some inequalities of the Ostrowski type for functions (of two variables) differentiable on the coordinates were established. In this paper, we extend these results to an arbitrary time scale by means of a parameter λ∈0,1. The aforementioned results are regained for the case when the time scale T=R. Besides extension, our results are employed to the continuous and discrete calculus to get some new inequalities in this direction

Simpson’s type inequalities for strongly (s,m)-convex functions in the second sense and applications

Some new inequalities of Simpson’s type for functions whose third derivatives in absolute value at some powers are strongly (s,m)- convex in the second sense are provided. An application to the Simpson’s quadrature rule is also provided

Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown

The outbreak of the coronavirus disease (COVID-19) has caused a lot of disruptions around the world. In an attempt to control the spread of the disease among the population, several measures such as lockdown, and mask mandates, amongst others, were implemented by many governments in their countries. To understand the effectiveness of these measures in controlling the disease, several mathematical models have been proposed in the literature. In this paper, we study a mathematical model of the coronavirus disease with lockdown by employing the Caputo fractional-order derivative. We establish the existence and uniqueness of the solution to the model. We also study the local and global stability of the disease-free equilibrium and endemic equilibrium solutions. By using the residual power series method, we obtain a fractional power series approximation of the analytic solution. Finally, to show the accuracy of the theoretical results, we provide some numerical and graphical results

New Bounds of Ostrowski–Gruss Type Inequality for (k + 1) Points on Time Scales

The aim of this paper is to present three new bounds of the Ostrowski--Gr\"uss type inequality for points $x_0,x_1,x_2,\cdots,x_k$ on time scales. Our results generalize result of Ng\^o and Liu, and extend results of Ujevi\'c to time scales with $(k+1)$ points. We apply our results to the continuous, discrete, and quantum calculus to obtain many new interesting inequalities. An example is also considered. The estimates obtained in this paper will be very useful in numerical integration especially for the continuous case.</p

A Parameter-Based Ostrowski–Grüss Type Inequalities with Multiple Points for Derivatives Bounded by Functions on Time Scales

In this paper, we present some Ostrowski&#8315;Gr&#252;ss-type inequalities on time scales for functions whose derivatives are bounded by functions for k points via a parameter. The 2D versions of these inequalities are also presented. Our results generalize some of the results in the literature. As a by-product, we apply our results to the continuous and discrete calculus to obtain some interesting inequalities in this direction

Jensen-type inequalities on time scales for n-convex functions

In this paper, the authors establish some lower and upper bounds for the difference in the Edmundson-Lah-Ribarič inequality in time scales calculus that holds for the class of n-convex functions by utilizing some scalar inequalities obtained via Hermite's interpolating polynomial. In addition, the authors also establish different lower and upper bounds for the difference in the Jensen inequality as a byproduct from the results of the Edmundson-Lah-Ribarič inequality. The main results are applied to obtain new converse inequalities for generalized means and power means in the time scale settings

Some new k-Riemann–Liouville fractional integral inequalities associated with the strongly η-quasiconvex functions with modulus μ≥0 μ≥0\mu\geq0

Abstract A new class of quasiconvexity called strongly η-quasiconvex function was introduced in (Awan et al. in Filomat 31(18):5783–5790, 2017). In this paper, we obtain some new k-Riemann–Liouville fractional integral inequalities associated with this class of functions. For specific values of the associated parameters, we recover results due to Dragomir and Pearce (Bull. Aust. Math. Soc. 57:377–385, 1998), Ion (Ann. Univ. Craiova, Math. Sci. Ser. 34:82–87, 2007), and Alomari et al. (RGMIA Res. Rep. Collect. 12(Supplement):Article ID 14, 2009)

New time scale generalizations of the Ostrowski-Grüss type inequality for k points

Abstract Two Ostrowski-Grüss type inequalities for k points with a parameter λ ∈ [ 0 , 1 ] $\lambda\in[0, 1]$ are hereby presented. The first generalizes a recent result due to Nwaeze and Tameru, and the second extends the result of Liu et al. to k points. Many new interesting inequalities can be derived as special cases of our results by considering different values of λ and k ∈ N $k\in\mathbb{N}$ . In addition, we apply our results to the continuous, discrete, and quantum time scales to obtain several novel inequalities in this direction