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Hölder regularity for non-autonomous fractional evolution equations

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This paper concerns a Hölder regularity result for non-autonomous fractional evolution equations (NFEEs) of the form \(^C\!D^\alpha _t u(t)+A(t)u(t)=f(t)\) in the sense of Caputo’s fractional derivative. Under the assumption of the Acquistapace-Terremi conditions, we get a representation of solution that is closer to standard integral equation. A pair of families of solution operators will be constructed in terms of the Mittag-Leffler function, the Mainardi Wright-type function, the analytic semigroups generated by closed dense operator \(A(\cdot )\) and two variation of parameters formulas. By a suitable definition of classical solutions, the solvability of the Cauchy problem is established. Moreover, we also prove the Hölder regularity of classical solutions.

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The work was supported by National Natural Science Foundation of China (12101142, 12071396).

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Correspondence to Yong Zhou.

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He, J.W., Zhou, Y. Hölder regularity for non-autonomous fractional evolution equations. Fract Calc Appl Anal 25, 378–407 (2022).

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