Abstract
In this paper, some explicit bounds on solutions to a class of new power nonlinear Volterra-Fredholm type dynamic integral inequalities on time scales are established, which can be used as effective tools in the study of certain dynamic equations. Application examples are also given.
Highlights
1 Introduction The calculus on time scales, which was initiated by Hilger in [ ], has received considerable attention in recent years due to its broad applications in economics, population’s models, quantum physics and other science fields
In the past years, there has been much research activity concerning Volterra integral equations and the dynamic integral inequalities on time scales which usually can be used as handy tools to study the qualitative theory of dynamic integral equations and dynamic equations on time scales
2 Preliminaries In what follows, T is an arbitrary time scale, Crd denotes the set of rd continuous functions
Summary
The calculus on time scales, which was initiated by Hilger in [ ], has received considerable attention in recent years due to its broad applications in economics, population’s models, quantum physics and other science fields.In the past years, there has been much research activity concerning Volterra integral equations and the dynamic integral inequalities on time scales which usually can be used as handy tools to study the qualitative theory of dynamic integral equations and dynamic equations on time scales. Nonlinear Volterra-Fredholm type dynamic integral inequalities on time scales have been paid little attention to. Various Volterra-Fredholm type inequalities including continuous and discrete versions have been established.
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