Vector-valued laplace transforms and cauchy problems

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On fractional resolvent operator functions (2010, background): “Moreover, A is just the generator of T (see [ 2 , 17]).”
Distributed-order fractional diffusions on bounded domains (2009, background): “ded, strongly continuous semigroup T(t) with generator Lon some Banach space H, the Cauchy problem ∂u(t,x)/∂t= Lu(t,x) with u(0,x) = f(x) has solution u(t,x) = T(t)f(x) for any initial condition f ∈ H[3]. One important special case is the pseudo-diﬀerential operator Lu(t,x) = Xd i,j=1 aij(x) ∂2u(t,x”
Extension problem and fractional operators: semigroups and wave equations (2012, background): “Arendt in [1], and of fractional order by M.”
Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives ✩ (2012, methodology): “4 in [3] shows that v ∈ C([0, T ];X).”
Almost periodic solutions to some semilinear non-autonomous thermoelastic plate equations (2009, neutral): “[5,7,9,16,17,27,30] for details.”