Fractional differentiation and its applications

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Fractional differentiation, or non-integer differentiation, emerged in the early days of calculus, with Leibniz and L’Hospital discussing half-order derivatives in 1695. Over the years, prominent mathematicians and physicists, including Abel, Liouville, Riemann, Grunwald, and Letnikov, explored fractional integrals and derivatives primarily from a theoretical standpoint. By the early 20th century, only a few applications had been introduced, notably by O. Heaviside and A. Gemant, who created fractional models for electrical and mechanical engineering. Despite these contributions, fractional differentiation remained largely unknown to applied scientists until recent decades, when interest surged in systems governed by fractional differential equations. A growing scientific community has revealed that many real physical systems, particularly those exhibiting long memory or hereditary behavior, are effectively described by fractional differential equations. Today, fractional differentiation is crucial in diverse fields such as biology, control theory, economics, electrical engineering, and more. The first IFAC workshop on Fractional Differentiation and its Applications took place in 2004 in Bordeaux, France, uniting experts to discuss current research and methodologies. This book comprises three parts, featuring articles from the workshop that present the latest research and industrial applications of fractional differentiation,