Maximal Regularity for Fractional Cauchy Equation in Hölder Space and Its Approximation

Abstract We derive the well-posedness and maximal regularity of the fractional Cauchy problem in Hölder space C 0 γ ⁢ ( E ) {C_{0}^{\gamma}(E)} . We also obtain the existence and stability of new implicit difference schemes for the general approximation to the nonhomogeneous fractional Cauchy problem. Our analysis is based on the approaches of the theory of β-resolvent families, functional analysis and numerical analysis.

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