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Zbl 1217.34006
Ashyralyev, Allaberen
Well-posedness of the Basset problem in spaces of smooth functions. (English)
[J] Appl. Math. Lett. 24, No. 7, 1176-1180 (2011). ISSN 0893-9659

Summary: We consider the initial value problem for the fractional differential equation $$\frac{du(t)}{dt} + D_t^{\frac12}u(t) + Au(t) = f(t), \quad 0 < t < 1, \quad u(0)=0$$ in a Banach space $E$ with the strongly positive operator $A$. The well-posedness of this problem in spaces of smooth functions is established. In practice, the coercive stability estimates for the solution of problems for $2m$-th order multidimensional fractional parabolic equations and one-dimensional fractional parabolic equations with nonlocal boundary conditions in the space variable are obtained.

MSC 2000:: *34A08
34G10 Linear ODE in abstract spaces
35K90 Abstract parabolic evolution equations

Keywords: fractional parabolic equation; Basset problem; well-posedness; coercive stability

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