[PDF] Top 20 Aumann Integral on Time Scales

... the Aumann ∆ -integral on time scales, the paper contributes to the theory of time scales, more specifically, for the integration on time ...The Aumann ... See full document

... Continuous fractional calculus is a field of mathematic study that grows out of the traditional definitions of the calculus integral and derivative operators. Fractional differ- entiation has played an important ... See full document

... These kinds of inequalities have many applications, when one wants to study the exis- tence and uniqueness of the solutions of a differential equation (see [33–35]). The results of our research depend on the law that ... See full document

... diamond-α integral and diamond integral which is defined as an ‘approximate’ symmetric integral on time scales, respectively [, –]; in Section , we give the main results; in Section ... See full document

... a time scale; that is, T is an arbitrary nonempty closed subset of real ...of time scales, which can also be found in [–], and of delta, nabla and diamond-α dynamic ... See full document

... several integral inequalities and studied the boundedness properties of some nonlinear dynamic equations, one of which we present below for convenience of the ...of time scales; see Bohner and ... See full document

... on time scales 12–17. However, only 10, 11 have studied integral inequalities useful in the theory of partial dynamic equations on time scales, as far as we ...nonlinear integral ... See full document

... on time scales. For incredible research on the theory of time scales, we suggest the peruser to [6] and the paper presenting nabla subsidiaries by Atici and Guseinov ... See full document

... Boundary value problem (BVP) for ordinary differential equations arise in different areas of applied mathematics and physics and so on, the existence and multiplicity of positive solutions for such problems have become ... See full document

... diamond-alpha integral Hölder’s inequalities on time scales are proposed and the related theorems and corollaries are ...same time, we also give the relevant conclusions and proof of n-tuple ... See full document

... A time scale is an arbitrary nonempty closed subset of the real numbers. In this paper, T denotes an arbitrary time scale. On T, we define the forward and backward jump operators s Î (T, T), and r Î (T, T) ... See full document

... type integral inequalities on time scales, which extend some known inequalities and provide a handy tool for deriving bounds of solutions of retarded dynamic equations on time ...the ... See full document

... on time scales have recently received considerable ...time scales. We prove a generalized version of Jensen’s inequality on time scales via the diamond-α integral and ... See full document

... of time scales in his doctoral dissertation, which resulted in his seminal paper in ...concerning time scales and dynamic equations on time scales can be found in the literature ... See full document

... certain dynamic equations on time scales. From the corollaries in Section , one can see the established inequalities unify continuous and discrete analysis. Finally, we note that the process of Theorems ... See full document

... type integral in- equalities on time ...the integral inequalities considered in this paper involve the retarded term, which results in difficulties in the estimation on the explicit bounds of unknown ... See full document

... fundamental integral inequalities used in the theory of differential and integral equations on time ...some time scale Pachpatte- type inequalities by extending some continuous inequalities ... See full document

... In this section, we indicate some applications of our results to obtain the estimates of the solutions of certain integral equations for which inequalities obtained in the literature thus far do not apply ... See full document

... In this paper, we investigate some nonlinear integral inequalities on time scales, which unify and extend some inequalities established by Pachpatte in [9]. The obtained inequal- ities can be used as ... See full document

... of integral inequalities on time scales with ‘maxima’ are established, which can be used as a handy tool in the investigation of making estimates for bounds of solutions of dynamic equations on ... See full document