@article{Albalawi2025, 
author = {Wedad Albalawi and Muhammad Imran Liaqat and Kottakkaran Sooppy Nisar and Abdel-Haleem Abdel-Aty},
title = {Qualitative study of Caputo Erdélyi-Kober stochastic fractional delay differential equations},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {8277-8305},
keywords = {Caputo Erdélyi-Kober derivatives, stochastic processes, existence and uniqueness, inequalities},
url = {https://www.sciopen.com/article/10.3934/math.2025381},
doi = {10.3934/math.2025381},
abstract = {We present new results on the well-posedness and time regularity of solutions to stochastic fractional delay differential equations (SFDDEs) using the Caputo-Erdélyi-Kober fractional derivative. Additionally, we prove the averaging principle. We establish all results in the        p  th moment, which generalizes the case        p    =  2. First, by applying fixed-point theory (FPT), we prove that the solution exists, is unique, and continuously depends on the initial values as well as the fractional derivative. Second, we establish a smoothness theorem for the solution and demonstrate that the solution of the original system converges to the averaged system in the        p  th moment. Finally, to support our theoretical findings, we present illustrative examples.}
}