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Geometric and physical interpretation of fractional integration and fractional differentiation. (English) Zbl 1042.26003
The author offers geometric visualizations (based on a technique called “shadows on the walls”) and physical interpretations (based on relationships between “individual time” and “cosmic time”) of important types of fractional differentiation and integration. He considers in detail the Riemann-Liouville fractional integral and derivative, the Caputo fractional derivative,the potentials of Riesz and Feller, and indicates analogues to more general convolution integrals of Volterra type and to Stieltjes integrals. While the geometric interpretations give illuminating insights into the meaning and way of acting of the operators considered, the physical interpretations presented seem to the reviewer to be of a more speculative character.

26A33Fractional derivatives and integrals (real functions)
44A35Convolution (integral transforms)
26A42Integrals of Riemann, Stieltjes and Lebesgue type (one real variable)
83C99General relativity
45D05Volterra integral equations
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