In this paper, space-time stochastic fractional reaction-diffusion equations (SFRDEs) driven by colored noise are investigated. Our first goal is to verify the existence, uniqueness, and boundedness of the solution. The next purpose, which is our main concern, is to investigate the stability in the fractional order \(\alpha \) of the solution and the convergence result when \(\alpha \rightarrow 1^-\) . More precisely, we prove that the solution depends continuously on the diffusion order \(\alpha \) , show in detail the exponent of the Hölder continuity, and prove that the solution of the fractional problem converges to the solution of the classical one. Despite the importance of such problems in modeling, to the best of our knowledge, no results have been reported so far on the stability with respect to the fractional order and the convergence for SFRDEs driven by colored noise. Our current paper is inspired by a recent work by M. Foondun [Remarks on a fractional-time stochastic equation. Proc. Amer. Math. Soc. 149 (2021), no. 5, 2235–2247].
