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The spectral accuracy of the Petrov\u2013Galerkin-based approach is only\nverified by numerical tests without theoretical justification.\nImplementation details are provided for both schemes, together with\na series of numerical examples to show the efficiency of the proposed methods.<\/jats:p>","DOI":"10.1515\/cmam-2017-0027","type":"journal-article","created":{"date-parts":[[2017,8,31]],"date-time":"2017-08-31T10:00:44Z","timestamp":1504173644000},"page":"43-62","source":"Crossref","is-referenced-by-count":43,"title":["M\u00fcntz Spectral Methods for the Time-Fractional Diffusion Equation"],"prefix":"10.1515","volume":"18","author":[{"given":"Dianming","family":"Hou","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing , Xiamen University , 361005 Xiamen , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Tanzil","family":"Hasan","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing , Xiamen University , 361005 Xiamen , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuanju","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing , Xiamen University , 361005 Xiamen , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,8,31]]},"reference":[{"key":"2023033115122822904_j_cmam-2017-0027_ref_001_w2aab3b7e1225b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"A. A.  Alikhanov,\nA new difference scheme for the time fractional diffusion equation,\nJ. Comput. Phys. 280 (2014), 424\u2013438.","DOI":"10.1016\/j.jcp.2014.09.031"},{"key":"2023033115122822904_j_cmam-2017-0027_ref_002_w2aab3b7e1225b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"F.  Amblard, A. C.  Maggs, B.  Yurke, A.  Pargellis and S.  Leibler,\nSubdiffusion and anomalous local viscoelasticity in actin networks,\nPhys. Rev. Lett. 77 (1996), no. 21, 4470\u20134473.","DOI":"10.1103\/PhysRevLett.77.4470"},{"key":"2023033115122822904_j_cmam-2017-0027_ref_003_w2aab3b7e1225b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"K. F.  Andersen and H. P.  Heinig,\nWeighted norm inequalities for certain integral operators,\nSIAM J. Math. Anal. 14 (1983), no. 14, 834\u2013844.","DOI":"10.1137\/0514064"},{"key":"2023033115122822904_j_cmam-2017-0027_ref_004_w2aab3b7e1225b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"D.  Baffet and J. S.  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