Electron. J. Diff. Equ., Vol. 2013 (2013), No. 240, pp. 1-14.

Solutions to nonlocal fractional differential equations using a noncompact semigroup

Shaochun Ji, Gang Li

This article concerns the existence of solutions to nonlocal fractional differential equations in Banach spaces. By using a type of newly-defined measure of noncompactness, we discuss this problem in general Banach spaces without any compactness assumptions to the operator semigroup. Some existence results are obtained when the nonlocal term is compact and when is Lipschitz continuous.

Submitted August 22, 2013. Published October 29, 2013.
Math Subject Classifications: 26A33, 34G20.
Key Words: Fractional differential equations; nonlocal conditions; measure of noncompactness.

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Shaochun Ji
Faculty of Mathematics and Physics
Huaiyin Institute of Technology
Huaian 223003, China
email: jiscmath@gmail.com
Gang Li
School of Mathematical Science
Yangzhou University
Yangzhou 225002, China
email: gli@yzu.edu.cn

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