This paper is intended to study the oscillatory behaviour of solutions of the higher order nonlinear neutral type functional dynamic equation with oscillating coefficients of the following form: [y(t) + p(t)y (τ(t))] n + m ∑ i=1 qi(t)fi (y (φi(t))) = s(t) where n ≥ 2. We obtain sufficient conditions for oscillatory behaviour of its solutions. Our results complement the oscillation results for n...

Stochastic differential equations and the Black-Scholes PDE. We derived the BlackScholes formula by using arbitrage (risk-neutral) valuation in a discrete-time, binomial tree setting, then passing to a continuum limit. This section explores an alternative, continuoustime approach via the Ito calculus and the Black-Scholes differential equation. This material is very standard; I like Wilmott-How...

In the present paper, the mathematical model of a test case central heating system is developed in the form of a nonlinear neutral time delay model which in turn is simplified to a neutral time delay model with constant time delay. In the process it is shown that the influence of the delay is significant, thus its incorporation to the model is of high importance. A PI controller is derived to c...

In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

A difference equation is presented to describe traffic flow on a highway. The difference equation model is derived from the optimal velocity models formulated in terms of the differential equations. It is compared with the differential equation models. We investigate phase transitions among the freely moving phase, the coexisting phase in which jams appear, and the uniform congested phase. The ...