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Existence of fuzzy fractional stochastic differential system with impulses

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Abstract

Stochastic differential equations represent equipment in modeling of a dynamic systems operating with fuzzy settings driven by stochastic noise. In this manuscript, a new kind of equation, namely fuzzy fractional stochastic differential system (FSDS) is proposed. It is defined by stochastic integral of a fuzzy process with respect to the m-dimensional Brownian motion. In this paper, the existence and uniqueness results are obtained for impulsive fuzzy FSDS with granular derivative using contraction principle. Finally, we provide a numerical example for the effectiveness of the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, The Gandhigram Rural Institute, Deemed to be University, Gandhigram, 624 302, Dindigul, Tamil Nadu, India

    J. Priyadharsini & P. Balasubramaniam

Authors
  1. J. Priyadharsini
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  2. P. Balasubramaniam
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Correspondence to P. Balasubramaniam.

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Communicated by Rosana Sueli da Motta Jafelice.

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Priyadharsini, J., Balasubramaniam, P. Existence of fuzzy fractional stochastic differential system with impulses. Comp. Appl. Math. 39, 195 (2020). https://doi.org/10.1007/s40314-020-01229-0

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  • DOI: https://doi.org/10.1007/s40314-020-01229-0

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