Qualitative analysis of A.P.A. solution for fractional order neutral stochastic evolution equations driven by G-Brownian motion

A. D. Nagargoje, V. C. Borkar, R. A. Muneshawar

Abstract


In this paper, we will analyses the square mean almost pseudo automorphic mild solution for fractional order equation,

(1) c0Dαγ [ℵ(γ)−D(γ,ℵ(γ))] = [Aℵ(γ) +φ(γ,ℵ(γ))]dγ + ϕ(γ,ℵ(γ))d<B>(γ) + ψ(γ,ℵ(γ))dB(γ), γ∈R

where A(γ) : D(A(γ)) ⊂ L 2 G (F) → L 2 G (F) is densely closed linear operator and the functions D, φ, ϕ and ψ: L2G(F) → L2G(F) are jointly continuous. We drive square mean almost pseudo automorphic mild solution for fractional order neutral stochastic evolution equations driven by G-Brownian motion is obtain by using evolution operator theorem and fixed point theorem. Moreover, we prove that this mild solution of equation (1) is unique.


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Published: 2022-02-28

How to Cite this Article:

A. D. Nagargoje, V. C. Borkar, R. A. Muneshawar, Qualitative analysis of A.P.A. solution for fractional order neutral stochastic evolution equations driven by G-Brownian motion, J. Math. Comput. Sci., 12 (2022), Article ID 100

Copyright © 2022 A. D. Nagargoje, V. C. Borkar, R. A. Muneshawar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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