An extension of Borel-Laplace methods and monomial summability
  In this paper we will show that monomial summability can be characterized using Borel-Laplace like integral transformations depending of a parameter $0<s<1$. We will apply this result to prove 1-summability in a monomial of formal solutions of a family of partial differential equations. 
Sergio A. Carrillo, Jorge Mozo-Fern\'andez
math.CV