Approximate Controllability of a Neutral Stochastic Fractional Integro-Differential Inclusion with Nonlocal Conditions

Alka Chadha () and Dwijendra N. Pandey ()
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Alka Chadha: Indian Institute of Technology Roorkee
Dwijendra N. Pandey: Indian Institute of Technology Roorkee

Journal of Theoretical Probability, 2018, vol. 31, issue 2, 705-740

Abstract: Abstract This paper discusses the approximate controllability of a neutral functional integro-differential inclusion involving Caputo fractional derivative in a Hilbert space under the assumptions that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of neutral fractional stochastic functional integro-differential inclusions are formulated and established by utilizing stochastic analysis theory, fractional calculus and the technique of fixed point theorem with analytic compact resolvent operator. An example is also considered for illustrating the discussed theory.

Keywords: Fractional calculus; Controllability; Caputo derivative; Resolvent operator; Stochastic fractional differential inclusion; Neutral equation; Nonlocal conditions; Multivalued operators; 34K37; 34K40; 34K45; 35R11; 35R60; 45J05; 45K05; 60H15; 60H20 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-016-0732-2

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