Short memory fractional differential equations for new memristor and neural network design

Fractional derivatives hold memory effects, and they are extensively used in various real-world applications. However, they also need large storage space and cause poor efficiency. In this paper, some standard definitions are revisited. Then, short memory fractional derivatives and a short memory fractional modeling approach are introduced. Numerical solutions are given by the use of the predictor–corrector method. The short memory is adopted for fractional modeling of memristor, neural networks and materials’ relaxation property. Global stability conditions of variable-order neural networks are derived. The new features of short memory fractional differential equations are used to improve the performance of networks. The results are illustrated in comparison with standard ones. Finally, discussions are made about potential applications.