Sergei Rogosin, Maryna Dubatovskaya
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. The aim of the paper is to present the essence of these two important approaches, namely, those developed by Letnikov (or by Grünwald–Letnikov) and by Marchaud. We collect here the most significant results for the corresponding fractional derivatives, compare these constructions, and highlight their roles in Fractional Calculus and its applications. Letnikov's work attempts to refine the definition of Liouville by challenging the assumption that the general definition of fractional derivatives can be applied solely to functions represented by convergent Dirichlet type series. This paper provides a comprehensive comparison of the two approaches, discusses their mathematical foundations, and emphasizes their implications in the broader context of fractional derivatives within mathematical analysis.
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title={Letnikov vs. Marchaud: A Survey on Two Prominent Constructions of Fractional Derivatives},
author={Sergei Rogosin and Maryna Dubatovskaya},
year={2017},
language={English}
}TY - JOUR TI - Letnikov vs. Marchaud: A Survey on Two Prominent Constructions of Fractional Derivatives AU - Sergei Rogosin AU - Maryna Dubatovskaya PY - 2017 LA - English ER -
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