Fractional derivative has a history as long as that of classical calculus, but it is much less popular than it should be. What is the physical meaning of fractional derivative? This is still an open problem. In modeling various memory phenomena, we observe that a memory process usually consists of two stages. One is short with permanent retention, and the other is governed by a simple model of fractional derivative. With the numerical least square method, we show that the fractional model perfectly fits the test data of memory phenomena in different disciplines, not only in mechanics, but also in biology and psychology. Based on this model, we find that a physical meaning of the fractional order is an index of memory.

No abstract

A facile and green method was developed to synthesize the graphene-carbon nanotubes (Gr-CNTs) nanocomposite with a sandwich lamination structure. Pt nanoparticles were loaded on the as-synthesized Gr-CNTs nanocomposite to prepare an electrochemical sensor for determining bisphenol A (BPA) in thermal printing paper. The electrochemical behavior of BPA on the Pt/Gr-CNTs nanocomposite was investigated by cyclic voltammetry (CV) and chronocoulometry (CC). The direct determination of BPA was accomplished by using differential pulse voltammetry (DPV) under optimized conditions. The oxidation peak current was proportional to the BPA concentration in the range from 6.0 × 10(-8) to 1.0 × 10(-5) M and 1.0 × 10(-5) to 8.0 × 10(-5) M with a correlation coefficient of 0.987 and 0.998, respectively. The detection limit was 4.2 × 10(-8) M (S/N = 3). The fabricated electrode showed good reproducibility, stability and selectivity. The proposed method was successfully applied to determine BPA in thermal printing papers samples and the results were satisfactory.