Foundations for L-fractional partial differential equations

Develop rigorous theorems for L-fractional partial differential equations analogous to Caputo-based results, including existence, uniqueness, and representation via bivariate fractional power series.

Background

The paper notes a lack of studies on L-fractional PDEs. In the Caputo setting, formal solutions via bivariate fractional series exist, but rigorous theory remains to be developed for L-fractional operators.

References

Finally, what about fractional partial differential equations? There are no studies for the L-fractional derivative. In the Caputo context, formal solutions have been found in terms of bivariate fractional power series, but rigorous theorems are yet to be investigated.

— 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