Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation

A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and dieren tiation (i.e., integration and dieren tiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional integration and dieren tiation, the Caputo fractional dieren tiation, the Riesz potential, and the Feller potential. It is also generalized for giving a new geometric and physical interpretation of more general convolution integrals of the Volterra type. Besides this, a new physical interpretation is suggested for the Stieltjes integral.

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