A class of new nonlinear dynamic integral inequalities containing integration on infinite interval on time scales

Abstract

In this paper, we investigate some new nonlinear dynamic integral inequalities containing integration on infinite interval on time scales, which provide explicit bounds on unknown functions. Our results not only generalize some dynamic inequalities in related literature, but also are new even for the continuous and discrete time cases. Two examples are given to illustrate the present results.

Some generalized Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs

“…We have established several generalized Volterra-Fredholm-type dynamical integral inequalities in two independent variables on time scale pairs using an inequality introduced in [33]. As one can see, Theorems 3.1-3.4 generalize many known results in the literature.…”

“…During the last few years, a lot of dynamic inequalities have been extended by many authors. See [25][26][27][28][29][30][31][32][33][34][35][36][37]. For example, Anderson [28] considered the following nonlinear integral inequality in two independent variables on time scale pairs: © The Author(s) 2020.…”

Derivation of dynamical integral inequalities based on two-dimensional time scales theory

“…Here Ω is defined as in (18). The conclusion in (19) can be achieved from (25), (30), and (31). Details are omitted.…”

Lyapunov-Type Inequalities for Second-Order Boundary Value Problems with a Parameter

“…If we take α � 2 and λ � 1 in inequality (48), we obtain the following result. 46, satisfying boundary condition (13). en,…”