Subordination Principle for a Class of Fractional Order Differential Equations

Mathematics

Emilia Bazhlekova¹ 

[1] Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, Sofia 1113, Bulgaria; E-Mail

关键词: Riemann–Liouville fractional derivative;    C₀-semigroup of operators;    Mittag–Leffler function;    completely monotone function;    Bernstein function;   

DOI  :  10.3390/math3020412

来源: mdpi

【 摘 要 】

The fractional order differential equationu′(t)=Au(t)+γDtαAu(t)+f(t),t>0,u(0)=a∈Xis studied, where A is an operator generating a strongly continuous one-parameter semigroup on a Banach space X,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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland