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Mathematics 2019, 7(2), 209;

Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2)

Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Author to whom correspondence should be addressed.
Received: 26 January 2019 / Revised: 13 February 2019 / Accepted: 14 February 2019 / Published: 24 February 2019
Full-Text   |   PDF [309 KB, uploaded 24 February 2019]


This paper studies the existence of mild solutions and the compactness of a set of mild solutions to a nonlocal problem of fractional evolution inclusions of order α ( 1 , 2 ) . The main tools of our study include the concepts of fractional calculus, multivalued analysis, the cosine family, method of measure of noncompactness, and fixed-point theorem. As an application, we apply the obtained results to a control problem. View Full-Text
Keywords: fractional evolution inclusions; mild solutions; condensing multivalued map fractional evolution inclusions; mild solutions; condensing multivalued map
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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He, J.W.; Liang, Y.; Ahmad, B.; Zhou, Y. Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2). Mathematics 2019, 7, 209.

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