Qualitative analysis of A.P.A. solution for fractional order neutral stochastic evolution equations driven by G-Brownian motion
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.
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.
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), 100. https://doi.org/10.28919/jmcs/7061
BibTeX
@article{Nagargoje2022,
author = {Nagargoje, A. D. and Borkar, V. C. and Muneshawar, R. A.},
title = {Qualitative analysis of A.P.A. solution for fractional order neutral stochastic evolution equations driven by G-Brownian motion},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {100},
doi = {10.28919/jmcs/7061}
}