ABSTRACT:
Fractional differentiation, an extension of classical calculus, generalizes the concept of integer-order derivatives to non-integer or fractional orders. While the traditional derivative of a function measures its rate of change, fractional differentiation provides a means of describing memory, hereditary properties, and anomalous dynamics found in complex systems. This paper explores the foundations, definitions, and applications of fractional derivatives, emphasizing their theoretical significance and practical use in physics, engineering, control theory, and biological modeling. The article also reviews major formulations such as the Riemann–Liouville and Caputo derivatives and discusses their computational and pedagogical implications. By bridging the gap between classical calculus and real-world nonlocal phenomena, fractional differentiation has emerged as a vital mathematical tool in modern science.
Cite this article:
Harsukh Singh (2025). Fractional Differentiation in Calculus: Theory, Techniques, and Applications . Spectrum of Emerging Sciences, 5 (2) 77-81, DOI: https://doi.org/10.55878/SES2025-5-2-21
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