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Riemann-Liouville Operator

The operator of fractional integration is defined as

_aD_t^(-nu)f(t)=1/(Gamma(nu))int_a^tf(u)(t-u)^(nu-1)du

for nu>0 with _aD_t^0f(t)=f(t) (Oldham and Spanier 1974, Miller and Ross 1993, Srivastava and Saxena 2001, Saxena 2002).

See also

Fractional Integral

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References

Miller, K. S. and Ross, B. An Introduction to the Fractional Calculus and Fractional Differential Equations. New York: Wiley, 1993.Oldham, K. B. and Spanier, J. The Fractional Calculus: Integrations and Differentiations of Arbitrary Order. New York: Academic Press, 1974.Saxena, R. K.; Mathai, A. M.; and Haubold, H. J. "On Fractional Kinetic Equations." 23 Jun 2002. http://arxiv.org/abs/math.CA/0206240.Srivastava, H. M. and Saxena, R. K. "Operators of Fractional Integration and Their Applications." Appl. Math. and Comput. 118, 1-52, 2001.

Referenced on Wolfram|Alpha

Riemann-Liouville Operator

Cite this as:

Weisstein, Eric W. "Riemann-Liouville Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Riemann-LiouvilleOperator.html

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