Abstract
We know that interpolation spaces in terms of analytic semigroup have a significant role into the study of strict Hölder regularity of solutions of classical abstract Cauchy problem (ACP). In this paper, we first construct interpolation spaces in terms of solution operators in fractional calculus and characterize these spaces. Then we establish strict Hölder regularity of mild solutions of fractional order ACP.
Highlights
We recall the properties of the solution operators Sα(t), Tα(t) in fractional calculus in order to find the motivation behind constructing new interpolation spaces
We introduce two classes of interpolation spaces in terms of solution operators. We show that these interpolation spaces are identical with the classical real interpolation space
4 Strict regularity of mild solutions This section is devoted to establishing strict Hölder regularity results using the interpolation space constructed in the last section
Summary
Bazhlekova [10], in her precious thesis, studied strict Lp- regularity by introducing the concept of solution operators and using the resolvent representation of classical interpolation space DA(θ , p) for 1 < p < ∞. We analyze the following points: (I) constructing interpolation spaces in terms of solution operators Sα(t), Tα(t) of fractional ACP and characterize these spaces, (II) establishing the strict Hölder regularity (or maximal Hölder regularity) results for the problem (1.2) utilizing this new representation of interpolation space.
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