A new definition of fractional derivative

By Zhibao Zheng, Wei Zhao, Hongzhe Dai. International Journal of Non-Linear Mechanics, 2019

161 citations recorded by the source corpus.

Abstract In this paper, a new fractional derivative of the Caputo type is proposed and some basic properties are studied. The form of the definition shows that the new derivative is the natural extension of the Caputo one, and that it yields the Caputo derivative with designated memory length. By adaptively changing the memory length, the new definition is capable of capturing local memory effect in a distinct way, which is critical in modelling complex systems where the short memory properties has to be considered. Another attractive property of the new derivative is that it is naturally associated with the Riemann–Liouville definition and as a result, the well established Grunwald–Letnikov approach for numerically solving the fractional differential equation can be readily embedded to approximate the solution of differential equation that involves the new derivatives. Numerical simulations demonstrate the changeable memory effect of the new definition.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d89c1d86332ae6b96d0a74e1f1c7769dce447dfb

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Citations in the corpus

Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications (2017, background): “In [8], the authors introduced a fractional derivative with an exponential kernel which tends to the ordinary derivative as α tends to 1.”
Novel solution methods for initial boundary value problems of fractional order with conformable differentiation (2017, background): “Recently, [20-22] introduced a new fractional derivative called conformable derivative operator (CDO) and by the help of this operator, the behaviors of many scientific problems have been solved and some solution methods have been developed.”
Existence for fractional Dirichlet boundary value problem under barrier strip conditions (2017, background): “Recently, the new conformable fractional derivative definition given by [1, 14, 24] has many good properties which inspired us study problems with conformable fractional derivative.”