Letnikov vs. Marchaud: A Survey on Two Prominent Constructions of Fractional Derivatives

Abstract

In this survey paper, we analyze two constructions of fractional derivatives proposed by Aleksey Letnikov (1837–1888) and by André Marchaud (1887–1973), respectively. These derivatives play very important roles in Fractional Calculus and its applications.

Keywords

• fractional integrals and derivatives
• Grünwald–Letnikov approach
• Marchaud approach
• fractional differences
• Hadamard finite part