Fractional-Order Grey Prediction Method for Non-Equidistant Sequences

There are lots of non-equidistant sequences in actual applications due to random sampling, imperfect sensors, event-triggered phenomena, and so on. A new grey prediction method for non-equidistant sequences (r-NGM(1,1)) is proposed based on the basic grey model and the developed fractional-order non-equidistant accumulated generating operation (r-NAGO), and the accumulated order is extended from the positive to the negative. The whole r-NAGO deletes the randomness of original sequences in the form of weighted accumulation and improves the exponential law of accumulated sequences. Furthermore, the Levenberg–Marquardt algorithm is used to optimize the fractional order. The optimal r-NGM(1,1) can enhance the predicting performance of the non-equidistant sequences. Results of three practical cases in engineering applications demonstrate that the proposed r-NGM(1,1) provides the significant predicting performance compared with the traditional grey model

Analysis of cryptocurrencies adoption using fractional grey Lotka-Volterra models

Abstract: Solving analytically nonlinear dynamical system in continuous time scale is often problematic. The accumulation generating operations provide a tool of formulating a discrete dynamical form whose properties are relatively close to that of corresponding nonlinear systems. The present study discusses threes versions of 2- and 3- dimensional discrete Lotka-Volterra dynamical system with application to cryptocurrencies adoption. The application is interested on 3 cryptocurrencies namely Bitcoin, Litecoin and Ripple. The 2-dimensional application is on Bitcoin and Litecoin while the 3-dimensional application is on Bitcoin, Litecoin and Ripple. The dataset include records from 28-April-2013 to 10-February-2018 which provide forecasting values for Bitcoin and Litecoin through 2-dimensional study, while records from 7-August-2013 to 10- February-2018 provide forecasting values of Bitcoin, Litecoin and Ripple through 3-dimensional study. The thesis has produced four papers that have been published and presented in international conferences.Ph.D. (Mathematics