The Conformable Ratio Derivative

Citation data:

Vol: 17, Issue: 2

Publication Year:
2017
Usage 335
Downloads 229
Abstract Views 106
Repository URL:
https://scholar.rose-hulman.edu/rhumj/vol17/iss2/10
Author(s):
Camrud, Evan
Tags:
conformable derivative; fractional derivative
article description
This paper proposes a new definition for a conformable derivative. The strengths of the new derivative arise in its simplicity and similarity to fractional derivatives. An inverse derivative (integral) exists showing similar properties to fractional integrals. The derivative is scalable, and exhibits particular product and chain rules. When looked at as a function with a parameter, the ratio derivative Kα [f] of a function f converges pointwise to f as α → 0, and to the ordinary derivative as α → 1. The conformable derivative is nonlinear in nature, but a related operator behaves linearly within a power series and Fourier series. Furthermore, the related operator behaves completely fractionally when acting within an exponential-based Fourier series.