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.File in questo prodotto:
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