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In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < α < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.doi:10.4134/jkms.2014.51.6.1123 fatcat:erardzbwlza2tfd7qgkz4kqc74