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Analytical solution of the generalized Bagley-Torvik equation. (English) Zbl 1459.34037

Summary: In this paper, we investigate the generalized Bagley-Torvik equation with the fractional order \((0,2)\). With a novel max-metric containing a Caputo derivative, the existence and uniqueness of the solution to the initial value problem are derived. We obtain the analytical solutions in terms of the Prabhakar function and the Wiman function, and they expand the well-known results about the general Bagley-Torvik equation. Two examples are presented to illustrate the validity of our main results.

MSC:

34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
34K37 Functional-differential equations with fractional derivatives
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
74D10 Nonlinear constitutive equations for materials with memory
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