Null controllability of fractional stochastic delay integro-differential equations

Volume 19, Issue 3, pp 143--150 http://dx.doi.org/10.22436/jmcs.019.03.01

Publication Date: May 15, 2019 Submission Date: September 12, 2017 Revision Date: December 31, 2018 Accteptance Date: April 30, 2019

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Authors

Hamdy M. Ahmed - Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt. Mahmoud M. El-Borai - Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt. H. M. El-Owaidy - Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt. A. S. Ghanem - Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt.

Abstract

Sufficient conditions for exact null controllability of semilinear fractional stochastic delay integro-differential equations in Hilbert space are established. The required results are obtained based on fractional calculus, semigroup theory, Schauder's fixed point theorem and stochastic analysis. In the end, an example is given to show the application of our results.

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Keywords

• Fractional calculus
• null controllability
• fractional stochastic delay integrodifferential equation
• Schauder's fixed point theorem

MSC

•  26A33
•  60H10
•  34K50
•  93B05

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