Work

Qualitative study of Caputo Erdélyi-Kober stochastic fractional delay differential equations

Year: 2025

Type: article

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 $ \mathfrak{p} $th moment, which generalizes the case $ \mathfrak{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 $ \mathfrak{p} $th moment. Finally, to support our theoretical findings, we present illustrative examples.

Source: AIMS Mathematics

DOI: 10.3934/math.2025381

Authors: Wedad Albalawi, Muhammad Imran Liaqat, Kottakkaran Sooppy Nisar, Abdel-Haleem Abdel-Aty

Institutions: Princess Nourah bint Abdulrahman University, Government College University, Lahore, Prince Sattam Bin Abdulaziz University, University of Bisha

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: University of Bisha, Princess Nourah Bint Abdulrahman University