Conformable Derivative Reassessed: Time Reparametrization vs. Fractional Calculus
Analysis
This paper challenges the common interpretation of the conformable derivative as a fractional derivative. It argues that the conformable derivative is essentially a classical derivative under a time reparametrization, and that claims of novel fractional contributions using this operator can be understood within a classical framework. The paper's importance lies in clarifying the mathematical nature of the conformable derivative and its relationship to fractional calculus, potentially preventing misinterpretations and promoting a more accurate understanding of memory-dependent phenomena.
Key Takeaways
- •The conformable derivative is not a fractional derivative.
- •It's equivalent to classical differentiation with a time reparametrization.
- •Problems using the conformable derivative can be transformed into classical formulations.
- •Classical and established fractional derivatives offer a more faithful framework for modeling memory-dependent phenomena.
“The conformable derivative is not a fractional operator but a useful computational tool for systems with power-law time scaling, equivalent to classical differentiation under a nonlinear time reparametrization.”