TY  - JOUR
AU  - Albalawi, Wedad
AU  - Liaqat, Muhammad Imran
AU  - Nisar, Kottakkaran Sooppy
AU  - Abdel-Aty, Abdel-Haleem
PY  - 2025
TI  - Qualitative study of Caputo Erdélyi-Kober stochastic fractional delay differential equations
JO  - AIMS Mathematics
SP  - 8277
EP  - 8305
VL  - 10
IS  - 4
AB  - 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.
UR  - https://doi.org/10.3934/math.2025381
DO  - 10.3934/math.2025381