On chain rule for fractional derivatives

By Vasily E. Tarasov. 2016

191 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Valentina V. Tarasova
2. Vasily E. Tarasov
3. G. Em Karniadakis
4. Guofei Pang

In Modeling and Simulation

1. G. Em Karniadakis
2. Lu Lu
3. Valentina V. Tarasova
4. Vasily E. Tarasov
5. Guofei Pang
6. Zhiping Mao
7. Om Prakash Agrawal
8. Xuhui Meng

In Numerical Analysis

1. Valentina V. Tarasova
2. G. Em Karniadakis
3. Lu Lu
4. Guofei Pang
5. Vasily E. Tarasov
6. Om Prakash Agrawal
7. Dumitru Băleanu
8. Martin Ostoja-Starzewski

Citations in the corpus

• fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “A typical example is the fractional derivatives of our interest, whose chain rule, if any, takes the form of infinite series [50, 51, 52]; see Appendix A for comparison of chain rules for the integer-order and the fractional derivatives.”
• Elasticity for economic processes with memory: Fractional differential calculus approach (2016, background): “The violation the standard chain rule is one of the main properties of derivatives of non-integer orders [27].”
• Leibniz rule and fractional derivatives of power functions (2016, background): “Moreover, unusual properties of fractional-order derivatives such as a violation of the usual Leibniz rule, a deformations of the usual chain rule [41,42], a violation of the semigroup property, and other characteristic properties [43,44] allow us to describe new unusual properties of complex media ”