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Approximate Controllability for Stochastic Fractional Hemivariational Inequalities of Degenerate Type

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Abstract

This paper is mainly concerned with stochastic fractional hemivariational inequalities of degenerate (or Sobolev) type in Caputo and Riemann-Liouville derivatives with order (1, 2), respectively. Based upon some properties of fractional resolvent family and generalized directional derivative of a locally Lipschitz function, some sufficient conditions are established for the existence and approximate controllability of the aforementioned systems. Particularly, the uniform boundedness for some nonlinear terms, the existence and compactness of certain inverse operator are not necessarily needed in obtained approximate controllability results.

MSC 2010: Primary 93B05; Secondary 34A08, 93E03

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Authors and Affiliations

  1. School of Mathematics and Statistics, X, idian University Xi’an, 710071, Shaanxi, P. R. China

    Yatian Pei & Yong-Kui Chang

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  1. Yatian Pei
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  2. Yong-Kui Chang
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Correspondence to Yatian Pei.

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Pei, Y., Chang, YK. Approximate Controllability for Stochastic Fractional Hemivariational Inequalities of Degenerate Type. Fract Calc Appl Anal 23, 1506–1531 (2020). https://doi.org/10.1515/fca-2020-0075

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  • DOI: https://doi.org/10.1515/fca-2020-0075

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