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Fractional-order differential equations with memory and fractional-order relaxation-oscillation model. (English) Zbl 1006.34008
Summary: One of the main applications of the fractional calculus (integration and differentiation of arbitrary (fractional) order) is the modeling of intermediate processes. Here, the authors give a general model for the relaxation-oscillation process. A solution to this model is given explicitly and continuation to fractional-order relaxation, fractional-order a oscillation, relaxation and oscillation processes is be proved.

MSC:
34A30 Linear ordinary differential equations and systems, general
34G10 Linear differential equations in abstract spaces
34G20 Nonlinear differential equations in abstract spaces
26A33 Fractional derivatives and integrals
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