The general solution of impulsive systems with Riemann-Liouville fractional derivatives
Abstract In this paper, we study a kind of fractional differential system with impulsive effect and find the formula of general solution for the impulsive fractional-order system by analysis of the limit case (as impulse tends to zero). The obtained result shows that the deviation caused by impulses for fractional-order system is undetermined. An example is also provided to illustrate the result.
The modelling of short-term interest rates in emerging markets is an important research area, especially in view of the growth of new financial markets and of the financial securities traded in these countries. Over the last decade, a number of researchers have looked at different models of short-term interest rates. An important paper in this area is the study by Chan, Karolyi, Longstaff and Sanders (1992, CKLS hereafter), who considered various one-factor models nested in their general interest rate model. The CKLS general model captured various aspects of interest rate behaviour, including drift and mean reversion of interest rates. It also allowed for a general relationship between the level of interest rates and the volatility of rates. By imposing restrictions on these parameters, various well-known models in the literature that are used extensively by financial market operators can be utilized.