Joseph Liouville
Core Contributions
Liouville was a pioneer in the rigorous formalization of fractional calculus. In 1832, he gave the first rigorous definition of fractional integrals, establishing the analytical theoretical foundation of fractional calculus based on the method of expanding functions into exponential series.
Selected Works
| Year | Work / Article | Problem Addressed |
|---|---|---|
| 1832 | Mémoire sur quelques questions de géométrie et de mécanique | First rigorously defined fractional derivatives, proposing a method of fractional differentiation based on exponential series expansion |
| 1832 | Mémoire sur le calcul des différentielles à indices quelconques | Systematically established the operational rules for differentiation of arbitrary order, proving the fractional derivative formulas for power functions and exponential functions |
| 1834 | Mémoire sur une formule d'analyse | Connected fractional differentiation with the theory of integral equations, providing tools for the subsequent solution of Abel integral equations |