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.

Author Bio

Evan Camrud is a graduating senior mathematics and chemistry major, and music minor. He created this manuscript from an insight he had while researching fractional derivatives as they apply to quantum mechanics. Evan is actively involved as a member of his school's percussion ensemble, and enjoys composing pieces of music in his down time. Fans of instrumental cover songs can listen to Evan's music on Spotify. His future plans are to pursue a Ph.D. in mathematics, in the area(s) of functional and harmonic analysis and/or operator theory.