Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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EXISTENCE AND UNIQUENESS OF SQUARE-MEAN PSEUDO ALMOST AUTOMORPHIC SOLUTION FOR FRACTIONAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY G-BROWNIAN MOTION

  • A.D. NAGARGOJE (P. G. Department of Mathematics N.E.S. Science College) ;
  • V.C. BORKAR (Department of Mathematics and Statistics Yeshwant Mahavidyalaya) ;
  • R.A. MUNESHWAR (P. G. Department of Mathematics N.E.S. Science College)
  • Received : 2021.06.19
  • Accepted : 2023.06.07
  • Published : 2023.09.30
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Abstract

In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as c0D𝛼𝜌 Ψ𝜌 = 𝒜(𝜌)Ψ𝜌d𝜌 + 𝚽(𝜌, Ψ𝜌)d𝜌 + ϒ(𝜌, Ψ𝜌)d ⟨ℵ⟩𝜌 + χ(𝜌, Ψ𝜌)dℵ𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

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Acknowledgement

The authors are thankful to the referees and editor for their valuable comments to improve this work.

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