Class Of Integral Inequalities Research Articles

A novel class of integral inequalities with graphical approach and diverse applications

ABSTRACT In this paper, we investigate a novel class of Hermite-Hadamard inequalities applicable to functions with h-convex absolute derivatives. Graphical representations are provided to bolster the validity of our key findings. Some limiting results of our main findings are discussed as corollaries. Furthermore, we establish error estimates in terms of trapezoid formulae for differences between generalized means.

New classes of unified fractional integral inequalities

<abstract><p>Many researchers in recent years have studied fractional integrals and derivatives. Some authors recently introduced generalized fractional integrals, the so-called unified fractional integrals. In this article, we establish certain new integral inequalities by employing the unified fractional integral operators. In fact, for a class of $ n $ $ (n\in\mathbb{N}), $ positive continuous and decreasing functions on $ [v_1, v_2], $ certain new classes of integral inequalities are discussed. The inequalities established in this manuscript are more general forms of the classical inequalities given in the literature. The existing classical inequalities can be rectified by imposing the conditions stated in remarks. By imposing certain conditions on $ \hbar $ and $ \Lambda $ available in the literature, many new forms of fractional integral inequalities can be produced.</p></abstract>

Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable

Saint-Venant equations describe the flow below a pressure surface in a fluid. We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. We formulate the extended operator in a linear convolution operator with a normalized function to study some important geometric behaviors. A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. Moreover, as an application, we determine the upper bound of the generalized fractional 2-dimensional Saint-Venant equations (2D-SVE) of diffusive wave including the difference of bed slope.

Some Nonlinear Integral Inequalities Connected with Retarded Terms on Time Scales

The objective of this research is to formulate a specific class of integral inequalities of Gronwall kind concerning retarded term and nonlinear integrals with time scales theory. Our results generate several new inequalities that reflect continuous and discrete form, as well as giving the unknown function an upper bound estimate. The effectiveness of such inequalities arises from the belief that it is widely relevant in unique circumstances where there is no valid utilization of various available inequalities. Applications are additionally represented to display the legitimacy of built-up hypotheses.

Partial Variable Stability for a Class of Nonlinear Systems with Time Delay

This article first gives a new class of integral inequalities. Then, as an application, the nonlinear neutral differential system with multiple delays is considered, and the trivial solution of the nonlinear neutral system with multiple delays is obtained. Uniform asymptotic Lipschitz stability. Obviously, the above system is a generalization of the traditional differential system. The purpose of this paper is to study the dual stability of neutral differential equations with delays, including equal asymptotically Lipschitz stability and uniformly asymptotic Lipschitz stability. The author uses the method of integral inequality to establish a double stability criterion. As a result, the local stability of differential equations is widely used in theory and practice, such as dynamic systems and control systems.

Some new inequalities for generalized fractional conformable integral operators

The present paper aims to establish certain new classes of integral inequalities for a class of n (nin mathbb{N}) positive continuous and decreasing functions by utilizing the generalized fractional conformable integral operators (FCIO) recently defined by Khan and Khan. From these results, we also derive several particular cases.

Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications

This paper is committed to introducing some Bihari type inequalities for scalar functions of one independent variable under an initial condition associated with an arbitrary time scale mathbb{T}. The integrals involve the maximum of an unknown function over a past time interval. We not only solve some new estimated bounds of a specific class of retarded and nonlinear dynamic inequalities but also derive and unify continuous inequalities along with the corresponding discrete analogs of some known results with ‘maxima’ on time scales. We illustrate some applications of the considered inequalities to represent the advantages of our work. The main results will be proved by utilizing some examination procedures and the basic technique of Keller’s chain rule on time scales.

Some fractional proportional integral inequalities

In the last few years, various researchers studied the so-called conformable integrals and derivatives. Based on that notion some authors used modified conformable derivatives (proportional derivatives) to generate nonlocal fractional integrals and derivatives, called fractional proportional integrals and derivatives, which contain exponential functions in their kernels. Our aim in this paper is to establish some new integral inequalities by utilizing the fractional proportional-integral operators. In fact, certain new classes of integral inequalities for a class of n (nin mathbb{N}) positive continuous and decreasing functions on [a,b] are presented. The inequalities presented in this paper are more general than the existing classical inequalities.

Some integral inequalities involving Saigo fractional integral operators

In this paper, the Saigo fractional integral operator is used to generate some new integral inequalities. By using the Saigo fractional integral operator, we also generate new classes of integral inequalities using a family of n positive functions defined on [a, b].

A Note on Relationship Between Two Classes of Integral Inequalities

This technical note firstly introduces two classes of integral inequalities with and without free matrices, respectively, and points out that they, although in different forms, are actually equivalent in the sense of conservatism, i.e., the two corresponding ones produce the same tight upper bounds. Secondly, the relationship between the method of integral inequalities with free matrices and the free-weighting matrix technique is intensively investigated. It is shown that these two different methods are actually equivalent in assessing the stability of time-delay systems.

A MAIN CLASS OF INTEGRAL INEQUALITIES WITH APPLICATIONS

In this paper, we define some integral transforms and obtain suitable bounds for them in order to introduce a main class of integral inequalities including Ostrowski and Ostrowski-Gr¨uss inequalities and various kinds of new integral inequalities. In this sense, we also introduce a three point quadrature formula and obtain its error bounds.

New synchronization criteria for complex delayed dynamical networks with sampled-data feedback control

This paper investigates the synchronization problem for a class of complex delayed dynamical networks (CDDNs) by using sampled-data feedback control. First, an augmented Lyapunov–Krasovskii function (LKF) is constructed, which contains two new triple integral terms to reduce the conservativeness. Second, improved synchronization criteria are proposed by combining reciprocally convex technique with a novel class of integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. Third, the desired sampled-data controllers can be achieved by solving a set of linear matrix inequalities (LMIs). Finally, three numerical simulation examples are presented to demonstrate the effectiveness and advantages of the proposed results.

On a class of integral inequalities of Hardy-Littlewood type

On a class of integral inequalities of Hardy-Littlewood type

On a new class of Hardy type inequalities

SynopsisIn this paper we establish a new class of integral inequalities which originate from the well-known Hardy's inequality. The analysis used in the proofs is quite elementary and is based on the idea used by Levinson to obtain generalisations of Hardy's inequality.

On a class of integral inequalities and their measure-theoretic consequences

On a class of integral inequalities and their measure-theoretic consequences

On a Class of Integral Inequalities

On a Class of Integral Inequalities

A note on a class of integral inequalities

AbstractA unified variational approach to a class of second-order integral in-equalities is presented. A special case recently considered in a different manner by Anderson, Arthurs and Hall (1) is recovered.

Best constants in a class of integral inequalities

Best constants in a class of integral inequalities