On Riemann-Liouville and Caputo Derivatives

By Changpin Li, Deliang Qian, YangQuan Chen. 2011

406 citations recorded by the source corpus.

Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann-Liouville (RL) derivative, one of mostly used fractional derivatives. Some important properties of the Caputo derivative which have not been discussed elsewhere are simultaneously mentioned. The partial fractional derivatives are also introduced. These discussions are beneficial in understanding fractional calculus and modeling fractional equations in science and engineering.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/952f95a15b53a1899794c449ec4d36bcb75a9624

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In Control and Systems Engineering

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order (2020, background): “3 ([27]) Let h ∈ Cα and α ≥ –1, then for the Riemann–Liouville (R–L) (leftsided) integral of left-sided order μ, μ > 0, we get”