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J. Korean Math. Soc. 2014; 51(6): 1123-1139
Printed November 1, 2014
https://doi.org/10.4134/JKMS.2014.51.6.1123
Copyright © The Korean Mathematical Society.
Upper and lower solution method for fractional evolution equations with order $1<\alpha<2$
Xiao-Bao Shu and Fei Xu
Hunan University, Wilfrid Laurier University
In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order $1<\alpha<2$ 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.
Keywords: fractional partial differential equation, mild solution, upper and lower solution method, Hausdorff measure of noncompactness
MSC numbers: 35R11
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