Role of the Laplace transform for L-fractional differential equations

Investigate whether the Laplace transform can be effectively used to solve L-fractional differential equations and under what precise hypotheses, given the additional nonlinearity introduced by the t^(1−α) factor.

Background

Whereas Caputo equations often benefit from Laplace-transform techniques, the t^1−α factor in L-fractional equations may complicate applicability. The authors note that this approach has not yet been verified for the L-fractional setting.