In this study we use the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of nonlinear conformable fractional PDEs. The proposed method yields a numerical approximate solution in the form of an infinite series that converges to a closed form solution, which is in many cases the exact solution. We inspect its efficiency in solving systems of CFPDEs by working on four different nonlinear systems. The results show that CFRDTM gave similar solutions to exact solutions, confirming its proficiency as a competent technique for solving CFPDEs systems. It required very little computational work and hence consumed much less time compared to other numerical methods.

The problem of the extraction of the relevant information for prediction purposes -in a Big Data time series context -is tackled. This issue is especially crucial when the forecasting activity involves macroeconomic time series, i.e. when one is mostly interested in finding leading variables and, at the same time, avoiding overfitted model structures. Unfortunately, the use of big data can cause dangerous overparametrization phenomena in the entertained models. In addition, two other drawbacks should be considered: firstly, human-driven handling of big data on a case-by-case basis is an impractical (and generally not viable) option and secondly, focusing solely on the raw time series might lead to suboptimal results. The presented approach deals with these problems using a twofold strategy: i) it expands the data in timescale domain, in the attempt to increase the likelihood of giving emphasis to possibly weak, relevant, signals and ii) carries out a multi-step dimension reduction procedure. The latter task is done by means of cross-correlation functions (whose employment will be theoretically justified) and a suitable objective function.

In this paper, we seek to find solutions of the local time fractional Telegraph equation (LTFTE) by employing the local time fractional reduced differential transform method (LTFRDTM). This method produces a numerical approximate solution having the form of an infinite series that converges to a closed form solution in many cases. We apply LTFRDTM on four different LTFTEs to examine the efficiency of the proposed method. The yielded results established the effectiveness of LTFRDTM as a reliable and solid approach for obtaining solutions of LTFTEs. The solutions coincided with the exact solution in the ordinary case when [Formula: see text]. It also required minimal amount of computational work and saved a lot of time.