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Existence of Solutions for Fractional Partial Neutral Stochastic Functional Integro-Differential Inclusions with State-Dependent Delay and Analytic Resolvent Operators

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Abstract

We investigate the existence of mild solutions for a class of fractional partial neutral stochastic functional integro-differential inclusions with state-dependent delay and analytic α-resolvent operators in Hilbert spaces. Sufficient conditions for the existence are established by using the nonlinear alternative of Leray–Schauder type for multivalued maps due to O’Regan and the fractional power of operators. An example is provided to illustrate the obtained theory.

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Authors and Affiliations

  1. Laboratory of Stochastic Models, Statistic and Applications, Tahar Moulay University, P.O. Box 138 En-Nasr, 20000, Saida, Algeria

    Toufik Guendouzi & Lamia Bousmaha

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  1. Toufik Guendouzi
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  2. Lamia Bousmaha
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Correspondence to Toufik Guendouzi.

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Guendouzi, T., Bousmaha, L. Existence of Solutions for Fractional Partial Neutral Stochastic Functional Integro-Differential Inclusions with State-Dependent Delay and Analytic Resolvent Operators. Vietnam J. Math. 43, 687–704 (2015). https://doi.org/10.1007/s10013-015-0154-y

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  • DOI: https://doi.org/10.1007/s10013-015-0154-y

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