On the solution of two-sided fractional ordinary differential equations of Caputo type (1701.04912v1)

Abstract: This paper provides well-posedness results and stochastic representations for the solutions to equations involving both the right- and the left-sided generalized operators of Caputo type. As a special case, these results show the interplay between two-sided fractional differential equations and two-sided exit problems for certain L\'evy processes.