Literatur Review: Sifat-Sifat Fundamental Turunan Fraksional Riemann–Liouville

Abstract

Fractional calculus is a generalization of classical calculus that extends the concepts of differentiation and integration to non-integer orders. One of the most widely used definitions is the Riemann–Liouville fractional derivative. This article is presented as a literature review aimed at examining the fundamental properties of the Riemann–Liouville fractional derivative based on the existing fractional calculus literature. The review is conducted through the examination and analysis of references discussing the definition and basic properties of this operator. The discussion focuses on the fractional derivatives of constant and identity functions, the constant multiple rule, the sum rule, the difference rule, linearity, and the power rule. The reviewed literature indicates that the Riemann–Liouville operator preserves several algebraic properties of the classical derivative, including the constant multiple rule, the sum rule, the difference rule, and linearity. However, it also exhibits distinctive characteristics, such as the fact that the fractional derivative of a constant function is not zero and the fractional derivative of the identity function is not one. This article provides a systematic overview of these properties, offering a structured understanding of the fundamental characteristics of the Riemann–Liouville fractional derivative as one of the key foundations of fractional calculus.