Closed-form representation of the iterated L-fractional integral operator LJ^m_α and convolution structure

Determine whether the iterated L-fractional integral operator LJ^m_α admits closed-form expressions, in particular whether LJ^m_α can be represented as a convolution operator analogous to the Caputo case, and consequently whether solutions depend on a new two-parameter Mittag-Leffler-type function.

Background

Unlike Caputo’s iterated integral operator, LJ^m_α lacks an established convolution structure, complicating explicit solution forms. The authors propose exploring closed forms and potential connections to a two-parameter Mittag-Leffler-type function to parallel Caputo-based results.