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Normalization of other fractional derivatives and impact of rescaling

Investigate whether rescaling other fractional derivatives (e.g., the A-fractional derivative) improves mathematical properties or applicability, and assess if fractional operators with continuous or bounded kernels benefit from including a (D^β t)^{-1} factor.

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Background

The L-fractional derivative normalizes the Caputo operator; analogously, the A-fractional derivative normalizes Riemann–Liouville. Exploring broader rescalings could address kernel-related issues and enhance modeling relevance.

References

Does it make sense to rescale other fractional derivatives? ... Would fractional operators Dβ with continuous or bounded kernels improve their applicability if a factor (Dβt)-1 is included?

— Theory on linear L-fractional differential equations and a new Mittag-Leffler-type function (2403.00341 - Jornet, 1 Mar 2024) in Section 8, Open Problems