Research Papers

Approximate Controllability of Partial Fractional Neutral Integro-Differential Inclusions With Infinite Delay in Hilbert Spaces

[+] Author and Article Information
Zuomao Yan

School of Mathematics and Statistics,
Lanzhou University,
Lanzhou, Gansu 730000, China
Department of Mathematics,
Hexi University,
Zhangye, Gansu 734000, China
e-mail: yanzuomao@163.com

Hongwu Zhang

Department of Mathematics,
Hexi University,
Zhangye, Gansu 734000, China
e-mail: hulin0828@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 4, 2012; final manuscript received May 5, 2015; published online June 30, 2015. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 11(1), 011001 (Jan 01, 2016) (15 pages) Paper No: CND-12-1166; doi: 10.1115/1.4030533 History: Received October 04, 2012; Revised May 05, 2015; Online June 30, 2015

We study the approximate controllability of a class of fractional partial neutral integro-differential inclusions with infinite delay in Hilbert spaces. By using the analytic α-resolvent operator and the fixed point theorem for discontinuous multivalued operators due to Dhage, a new set of necessary and sufficient conditions are formulated which guarantee the approximate controllability of the nonlinear fractional system. The results are obtained under the assumption that the associated linear system is approximately controllable. An example is provided to illustrate the main results.

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