## Real Analysis Exchange

### The s-dimensional Hausdorff integral and its physical interpretation

Shusheng Fu

#### Abstract

A relationship between the $s$-dimensional Hausdorff integral and the evolution with losses is established. Professor R. R. Nigmatullin showed that the evolution with loss can be described by a non-integer integral. This paper gives another way to describe the evolution. That is, the evolution can be expressed as Hausdorff integral.

#### Article information

Source
Real Anal. Exchange, Volume 21, Number 1 (1995), 308-316.

Dates
First available in Project Euclid: 3 July 2012

https://projecteuclid.org/euclid.rae/1341343247

Mathematical Reviews number (MathSciNet)
MR1377541

Zentralblatt MATH identifier
0856.26007

#### Citation

Fu, Shusheng. The s -dimensional Hausdorff integral and its physical interpretation. Real Anal. Exchange 21 (1995), no. 1, 308--316. https://projecteuclid.org/euclid.rae/1341343247

#### References

• K. J. Falconer, The geometry of fractal Sets, Cambridge Univ. Press, London and New York, 1985.
• H. Federer, Colloquium Lectures on geometric Measure theory, Bull. Amer. Math. Soc. 84, 1978.
• S. S. Fu, $\lambda$-power integrals on the Cantor type sets, to appear in Proc. Amer. Math. Soc..
• S. S. Fu, Hausdorff Calculus and Arc Length, submitted.
• B. B. Mandelbrot, The fractal geometry of nature, San Francisco, W. H. Freeman & Co., 1982.
• R. R. Nigmatullin, A fractional integral and its physical interpretation, Teoret. Met. Fiz, 90 no. 3 (1992), 354–368; Translation in Theoret. and Math. Phy, 90 no. 3 (1992), 242–251.
• B. S. Thomson, Differentiation bases on the real line, I and II, Real Analysis Exchange, 7 (1982–83), 67–208; 8 (1982–83) 278–442.