Approximate controllability of impulsive Hilfer fractional differential inclusions

Volume 10, Issue 2, pp 595--611 http://dx.doi.org/10.22436/jnsa.010.02.23

Publication Date: February 20, 2017 Submission Date: July 20, 2016

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Authors

Jun Du - School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China. - Department of Applied Mathematics, Huainan Normal University, Huainan 232038, P. R. China. Wei Jiang - School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China. Azmat Ullah Khan Niazi - School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China.

Abstract

In this paper, firstly by utilizing the theory of operators semigroup, probability density functions via impulsive conditions, we establish a new \(PC_{1-\nu}\)-mild solution for impulsive Hilfer fractional differential inclusions. Secondly we prove the existence of mild solutions for the impulsive Hilfer fractional differential inclusions by using fractional calculus, multi-valued analysis and the fixed-point technique. Then under some assumptions, the approximate controllability of associated system are formulated and proved. An example is provided to illustrate the application of the obtained theory

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Keywords

• Approximate controllability
• impulsive system
• Hilfer fractional differential inclusions
• multivalued maps
• fixed point theorem
• semigroup theory.

MSC

•  34A08
•  34A60
•  93B05

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