In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. T...

In this paper, the existence of limit cycles for the specific bilinear systems is explored. Based on the BellmanGronwall inequality approach, not only the exponentially stable limit cycles phenomenon of such systems can be certified but also the oscillation behaviors of such systems can be correctly predicted. Finally, a numerical example is provided to illustrate the feasibility and effectiven...

Variable-order fractional discrete calculus is a new and unexplored part of that provides extraordinary capabilities for simulating multidisciplinary processes. Recognizing this incredible potential, the scientific community has been researching variable-order applications to modeling engineering physical systems. This research makes contribution topic by describing establishing first generaliz...

<p style='text-indent:20px;'>This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where generator <inline-formula> <tex-math id="M1">\begin{document}$ g $\end{document}</tex-math> </inline-formula> satisfies weak stochastic-monotonicity condit...