Bernhard Riemann
Core Contributions
Riemann independently developed the definition of fractional integrals in his doctoral dissertation, constructing fractional-order operations starting from the lower limit of integration in a different manner. Riemann's definition was later systematically organized by Samko and others, forming the celebrated Riemann-Liouville fractional integral theory.
Selected Works
| Year | Work / Article | Problem Addressed |
|---|---|---|
| 1847 | Versuch einer allgemeinen Auffassung der Integration und Differentiation | Independently proposed the definition of fractional integrals starting from the lower limit of integration, laying the "Riemann" part of Riemann-Liouville fractional integrals |
| 1851 | Grundlagen für eine allgemeine Theorie der Functionen (Doctoral Dissertation) | Established the theoretical foundation of complex analysis; the integral methods contained therein were later extended to the fractional-order case |