3 papers
math.CA2018
Fractional derivative of composite functions: exact results and physical applications
Gavriil Shchedrin, Nathanael C. Smith, Anastasia Gladkina +1
We examine the fractional derivative of composite functions and present a generalization of the product and chain rules for the Caputo fractional derivative. These results are espe…
math-ph2017
Exact results for a fractional derivative of elementary functions
Gavriil Shchedrin, Nathanael C. Smith, Anastasia Gladkina +1
We present exact analytical results for the Caputo fractional derivative of a wide class of elementary functions, including trigonometric and inverse trigonometric, hyperbolic and…
math.NA2017
Expansion of fractional derivatives in terms of an integer derivative series: physical and numerical applications
Anastasia Gladkina, Gavriil Shchedrin, U. Al Khawaja +1
We use the displacement operator to derive an infinite series of integer order derivatives for the Grünwald-Letnikov fractional derivative and show its correspondence to the Rieman…