Abstract

By using stochastic analysis, fractional analysis, compact semigroups and the Schauder fixed-point theorem, we discuss the approximate boundary controllability of a nonlocal Hilfer fractional stochastic differential system with fractional Brownian motion and a Poisson jump. In addition, we establish the sufficient conditions for exact null controllability for the same problem. Finally, an example is given to illustrate the results obtained.

Details

Title
Boundary controllability of nonlocal Hilfer fractional stochastic differential systems with fractional Brownian motion and Poisson jumps
Author
Ahmed, Hamdy M 1   VIAFID ORCID Logo  ; El-Borai, Mahmoud M 2 ; M Elsaid Ramadan 3 

1  Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Egypt 
2  Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt 
3  Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt; Department of Mathematics, Faculty of Science, Islamic University, Madinah, Saudi Arabia 
Pages
1-23
Publication year
2019
Publication date
Feb 2019
Publisher
Springer Nature B.V.
ISSN
1687-1839
e-ISSN
1687-1847
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13662-019-2028-1
ProQuest document ID
2187005090
Copyright
Advances in Difference Equations is a copyright of Springer, (2019). All Rights Reserved., © 2019. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.