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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 \u03b2-resolvent families, functional analysis and numerical analysis.<\/jats:p>","DOI":"10.1515\/cmam-2018-0185","type":"journal-article","created":{"date-parts":[[2019,1,30]],"date-time":"2019-01-30T09:45:10Z","timestamp":1548841510000},"page":"779-796","source":"Crossref","is-referenced-by-count":13,"title":["Maximal Regularity for Fractional Cauchy Equation in H\u00f6lder Space and Its Approximation"],"prefix":"10.1515","volume":"19","author":[{"given":"Li","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences , Yangzhou University , Yangzhou, Jiangsu 225002 , P. R. China"}]},{"given":"Zhenbin","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences , Yangzhou University , Yangzhou, Jiangsu 225002 , P. R. China"}]},{"given":"Gang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences , Yangzhou University , Yangzhou, Jiangsu 225002 , P. R. China"}]},{"given":"Sergey","family":"Piskarev","sequence":"additional","affiliation":[{"name":"Scientific Research Computer Center , Lomonosov Moscow State University , Leninskie Gory , Moscow 119899 , Russia"}]}],"member":"374","published-online":{"date-parts":[[2019,1,30]]},"reference":[{"key":"2023033110105328552_j_cmam-2018-0185_ref_001_w2aab3b7e2813b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"A. A.  Alikhanov,\nA new difference scheme for the time fractional diffusion equation,\nJ. Comput. 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