Nonoscillation and Oscillation Theory for Functional Differential Equations

Predictive differential equations

“…The predictive differential equation we have introduced here can be thought of as a special case of functional differential equations or differential equations with shifted arguments [4]. However, it is of interest that a certain degree of non-locality on the time axes in the form of advance or delay can bring in complex behaviors to simple differential equations.…”

Oscillation of fractional order functional differential equations with nonlinear damping

“…Recently, research on oscillation of various equations including di erential equations, di erence equations, and dynamic equations on time scales has been a hot topic in the literature, and much e ort has already been put into establishing new oscillation criteria for these equations; see the monographs [22,23]. In these investigations, we notice that very little attention is paid to oscillation of fractional di erential equations.…”

Oscillation of nonlinear second-order neutral delay differential equations

“…The qualitative analysis of neutral differential equations is more difficult in comparison with that of ordinary differential equations; see, for instance, the monograph [1] and the paper [17]. Most oscillation criteria reported in the literature for equation (1.1) and its particular cases have been obtained under the assumptions that…”