The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional
integral as
where gamma function . From this equation, fractional
derivatives can also be defined.
See also Derivative ,
Fractional Derivative ,
Fractional Differential
Equation ,
Fractional Integral ,
Integral ,
Multiple Integral ,
Riemann-Liouville
Operator
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References Butzer, P. L. and Westphal, U. "An Introduction to Fractional Calculus." Ch. 1 in Applications
of Fractional Calculus in Physics Kilbas, A. A.; Srivastava, H. M.;
and Trujiilo, J. J. Theory
and Applications of Fractional Differential Equations. McBride, A. C. Fractional
Calculus. Nishimoto, K. Fractional
Calculus. Samko,
S. G.; Kilbas, A. A.; and Marichev, O. I. Fractional
Integrals and Derivatives. Oldham,
K. B. and Spanier, J. The
Fractional Calculus: Integrations and Differentiations of Arbitrary Order. Referenced on Wolfram|Alpha Fractional Calculus
Cite this as:
Weisstein, Eric W. "Fractional Calculus."
From MathWorld https://mathworld.wolfram.com/FractionalCalculus.html
Subject classifications
is the gamma function. From this equation, fractional
derivatives can also be defined.
