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Fractional calculus via functional calculus: Theory and applications. (English) Zbl 1026.47010

The paper demonstrates the power of the functional calculus definition of linear fractional differential operators via generalized Fourier transforms. The solutions are presented as convolutions of the input functions with the related impulse responses. Some examples are presented. The quality of the method is exemplified by comparing the numerical results with measurements.

MSC:

47A60 Functional calculus for linear operators
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74D05 Linear constitutive equations for materials with memory
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