@article{Albalawi2024, 
author = {Wedad Albalawi and Muhammad Imran Liaqat and Fahim Ud Din and Kottakkaran Sooppy Nisar and Abdel-Haleem Abdel-Aty},
title = {Well-posedness and Ulam-Hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivatives},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {12375-12398},
keywords = {conformable fractional derivative, pantograph fractional stochastic differential equations, well-posedness, Ulam-Hyers stability},
url = {https://www.sciopen.com/article/10.3934/math.2024605},
doi = {10.3934/math.2024605},
abstract = {One kind of stochastic delay differential equation in which the delay term is dependent on a proportion of the current time is the pantograph stochastic differential equation. Electric current collection, nonlinear dynamics, quantum mechanics, and electrodynamics are among the phenomena modeled using this equation. A key idea in physics and mathematics is the well-posedness of a differential equation, which guarantees that the solution to the problem exists and is a unique and meaningful solution that relies continuously on the initial condition and the value of the fractional derivative. Ulam-Hyers stability is a property of equations that states that if a function is approximately satisfying the equation, then there exists an exact solution that is close to the function. Inspired by these findings, in this research work, we established the Ulam-Hyers stability and well-posedness of solutions of pantograph fractional stochastic differential equations (PFSDEs) in the framework of conformable derivatives. In addition, we provided examples to analyze the theoretical results.}
}