The first-order differential equation of exponential relaxation can be generalized by replacing the time-derivative by a fractional derivative of Caputo type, more generally by an integral over such fractional derivatives, the order of differentiation being the variable of integration. We give an outline of the theory, show the form of solutions for a few examples and investigate the asymptotics near zero and near infinity.

Fractional relaxation of distributed order

MAINARDI, FRANCESCO
2006

Abstract

The first-order differential equation of exponential relaxation can be generalized by replacing the time-derivative by a fractional derivative of Caputo type, more generally by an integral over such fractional derivatives, the order of differentiation being the variable of integration. We give an outline of the theory, show the form of solutions for a few examples and investigate the asymptotics near zero and near infinity.
2006
Complex Mundi: Emergent Patterns in Nature
33
42
R. Gorenflo; F. Mainardi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/34979
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