Related papers: Generalizations of Gronwall-Bihari Inequalities on…

We establish some linear and nonlinear integral inequalities of Gronwall-Bellman-Bihari type for functions with two independent variables on general time scales. The results are illustrated with examples, obtained by fixing the time scales…

We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…

This paper aims to introduce Halanay type inequalities on time scales. By means of these inequalities we derive new global stability conditions for nonlinear dynamic equations on time scales. Giving several examples we show that beside…

We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.

In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.

We establish two nonlinear retarded integral inequalities. Bounds on the solution of some retarded equations are then obtained.

In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral…

In this paper we obtain the estimates on some dynamic integral inequalities in three variables which can be used to study certain dynamic equations. We give some applications to convey the importance of our result.

In this paper, we provide some new generalizations of Feng Qi type integral inequalities on time scales by using elementary analytic methods.

The goal of the present article is to offer a number of new retarded nonlinear inequalities of Gronwall, Bellman and Pachpatte kind for a class of integral and integro-differential equations. These inequalities generalize and provide new…

The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.

In this paper, some new Gronwall type inequalities involving iterated integrals are given.

In this paper, we propose a generalized Gronwall inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential equation involving the $\psi$-Hilfer fractional derivative…

We introduce more general concepts of Riemann-Liouville fractional integral and derivative on time scales, of a function with respect to another function. Sufficient conditions for existence and uniqueness of solution to an initial value…

We give a proposal to generalize the concept of the differential equations on time scales, such that they can be more appropriate for the analysis of real world problems, and give more opportunities to increase the theoretical depth of…

A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…

We consider the completely positive discretizations of fractional ordinary differential equations (FODEs) on nonuniform meshes. Making use of the resolvents for nonuniform meshes, we first establish comparison principles for the…

In this paper we obtain some weighted generalizations of Ostrowski type inequalities on time scales involving combination of weighted {\Delta}-integral means, i.e., a weighted Ostrowski type inequality on time scales involving combination…

In this paper, we formulate and prove Wendroff's inequalities on time scales. Next, we deduct some of Pachpatte's inequalities.

We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…