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 K&alpha [f] of a function f converges pointwise to f as &alpha &rarr 0, and to the ordinary derivative as &alpha &rarr 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.
Darin J. Ulness, Department of Chemistry, Concordia College
"The Conformable Ratio Derivative,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 17
, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol17/iss2/10