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Approximate Controllability of Fractional Semilinear Stochastic System of Order α∈ (1,2]

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Abstract

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in L p spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory.

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Authors and Affiliations

  1. Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, 248007, India

    Anurag Shukla

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    N Sukavanam & D. N. Pandey

Authors
  1. Anurag Shukla
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  2. N Sukavanam
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  3. D. N. Pandey
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Correspondence to Anurag Shukla.

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Shukla, A., Sukavanam, N. & Pandey, D.N. Approximate Controllability of Fractional Semilinear Stochastic System of Order α∈ (1,2]. J Dyn Control Syst 23, 679–691 (2017). https://doi.org/10.1007/s10883-016-9350-7

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  • DOI: https://doi.org/10.1007/s10883-016-9350-7

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