Abstract and Applied Analysis
Functional differential equations arise in many areas of science and technology: whenever a deterministic relationship involving some varying quantities and their rates of change in space and/or time (expressed as derivatives or differences) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time varies. In some cases, this differential equation (called an equation of motion) may be solved explicitly. In fact, differential equations play an important role in modelling virtually every physical, technical, biological, ecological, and epidemiological process, from celestial motion, to bridge design, to interactions between neurons, to interaction between species, to spread of diseases with a population, and so forth. Also many fundamental laws of chemistry can be formulated as differential equations and in economy differential equations are used to model the behavior of complex systems. However, the mathematical models can also take different forms depending on the time scale and space structure of the problem; it can be modeled by delay differential equations, difference equations, partial delay differential equations, partial delay difference equations, or the combination of these equations.
Copyright © 2015, Cemil Tunç et al.
Hindawi Publishing Corp.
Place of Publication
Islam, Muhammad; Tunc, Cemil; Benchohra, Mouffak; Lui, Bingwen; and Saker, Samir H., "Qualitative Theory of Functional Differential and Integral Equations" (2015). Mathematics Faculty Publications. 65.