Michele Caputo

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Michele Caputo
Born	(1927-05-05) May 5, 1927 (age 99) Ferrara, Italy
Education	University of Bologna
Known for	Caputo fractional derivative
Scientific career
Fields	Geophysics Geodesy Fractional calculus
Workplaces	University of Trieste Sapienza University of Rome Texas A&M University

Michele Caputo (5 May 1927-) is an Italian geophysicist, geodesist, and mathematician.

He is known for his formulation of the Caputo fractional derivative.

Education

Caputo obtained degrees in mathematics and physics from the University of Bologna.

Career

In his research on seismological Q-models, Caputo introduced a notion of fractional derivative which now bears his name. For a nonnegative integer ${\displaystyle m}$ and fractional part ${\displaystyle 0<z<1}$, the Caputo fractional derivative of order ${\displaystyle m+z}$ is defined by $${\displaystyle {\frac {\operatorname {d} ^{m+z}}{\operatorname {d} x^{m+z}}}\left[f\left(x\right)\right]={\frac {1}{\operatorname {\Gamma } \left(1-z\right)}}\int _{0}^{x}{\frac {f^{\left(m+1\right)}\left(t\right)}{\left(x-t\right)^{z}}}\,\operatorname {d} t}$$ provided that ${\displaystyle f}$ is smooth on ${\displaystyle (0,\infty )}$.

Caputo conducted geomagnetic, gravimetric, and glaciological research during the 1954 Italian Karakoram expedition.

References

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