# On the solution of two-sided fractional ordinary differential equations of Caputo type

## TL;DR

This paper investigates the well-posedness and stochastic representations of two-sided Caputo fractional differential equations, revealing their connection to exit problems for Lévy processes and expanding understanding of such equations.

## Contribution

It introduces new well-posedness results and stochastic representations for two-sided Caputo fractional differential equations, linking them to Lévy process exit problems.

## Key findings

- Established well-posedness for two-sided fractional equations
- Derived stochastic representations involving Lévy processes
- Connected two-sided fractional equations to exit problems

## 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.