Some Nonlinear Delay Volterra–Fredholm Type Dynamic Integral Inequalities on Time Scales

Abstract

We are devoted to studying a class of nonlinear delay Volterra–Fredholm type dynamic integral inequalities on time scales, which can provide explicit bounds on unknown functions. The obtained results can be utilized to investigate the qualitative theory of nonlinear delay Volterra–Fredholm type dynamic equations. An example is also presented to illustrate the theoretical results.

On some generalizations of nonlinear dynamic inequalities on time scales and their applications

“…and (49) Then as in the proof of previous theorem from (46) we see that the inequalities (25) and (26) hold for v 2 . From (50), (26) and the hypothesis (45). By using Lemma…”

“…The book on the subject of time scales by Bohner and Peterson [14] summarizes and organizes much of time scale calculus. During the past decade a number of dynamic inequalities have been established by some authors which are motivated by some applications, for example, when studying the behavior of solutions of certain class of dynamic equations on a time scale T. We refer the reader to [5,8,9,14,16,22,23,24,25,26,35,36,37,38,48,49,50] for contributions, and the references cited therein.…”

On some generalizations of dynamic Opial-type inequalities on time scales

“…During the last decade, many inequalities have been studied by different authors (see [1,2,[10][11][12][13][14]26] and the references cited therein).…”

A class of dynamic integral inequalities with mixed nonlinearities and their applications in partial dynamic systems

“…For the study of time scales theory, integral inequalities are usually used to investigate the boundedness of dynamic systems. In recent years, different types of integral inequalities have been widely studied [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For example, the sublinear integral inequality…”