Subordination Principle for a Class of Fractional Order Differential Equations
نویسندگان
چکیده
The fractional order differential equation u′(t) = Au(t) + γD t Au(t) + f(t), t > 0, u(0) = a ∈ X is studied, whereA is an operator generating a strongly continuous one-parameter semigroup on a Banach space X , D t is the Riemann–Liouville fractional derivative of order α ∈ (0, 1), γ > 0 and f is an X-valued function. Equations of this type appear in the modeling of unidirectional viscoelastic flows. Well-posedness is proven, and a subordination identity is obtained relating the solution operator of the considered problem and the C0-semigroup, generated by the operator A. As an example, the Rayleigh–Stokes problem for a generalized second-grade fluid is considered.
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