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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.

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