The applications based on models concerning fractional delay differential models influenced by stochastic behavior have gained great interest in physical and natural sciences. This paper employs contraction mapping in Banach spaces to validate the TE-U of a certain class of M-fractional SDDMs driven by SBM. For this aim, we establish some suitable Lipschitz constraints on the drift and the diffusion coefficients and employ a weighted normed space based on the space \({\text{{\rm H}}}p\) for \(p \geqslant 2\) . For convenience, BDGI estimates the stochastic terms in the desired proofs. The theoretical findings are followed by constructing a numerical step spectral method to provide approximate solutions to the suggested models. In this method, we organize steps to deal with the delay terms in subintervals, and the desired approximations in each subinterval are obtained using a collocation spectral mechanism, where the test functions are the orthogonal SLPs in which the problem is condensed into a group of computational simultaneous equations. For the stochastic term, the quantities of the SBM paths are assessed with the MATHEMATICA program. Moreover, the convergence study is confirmed for the presented approach to capture the behavior of approximations. Ultimately, applications of various forms are solved and shown in terms of tables, figures, and notations, whilst the obtained results emphasize the accuracy and validity of the constructed algorithm steps. The eloquent method formulation indicates the ability to use it in solving other types of fractional stochastic delay differential models that appear in various scientific and engineering domains.
