loading page

Extreme values of solution of Caputo-Hadamard uncertain fractional differential equation and applications
  • Hanjie Liu,
  • Yuanguo Zhu,
  • Liu He
Hanjie Liu
Nanjing University of Science and Technology
Author Profile
Yuanguo Zhu
Nanjing University of Science and Technology

Corresponding Author:ygzhu@njust.edu.cn

Author Profile
Liu He
Nanjing University of Science and Technology
Author Profile


Uncertain fractional differential equation (UFDE) is an useful tool for studying complex systems in uncertain environments. In this paper, we study the extreme value theorems of the solution to Caputo-Hadamard UFDEs and applications. A numerical algorithm for solving the numerical solution of a nonlinear Caputo-Hadamard UFDE is presented, the feasibility of the numerical algorithm is validated by numerical experiments. The extreme value theorems are applied to the financial markets, and the pricing formulas of the American option based on the new uncertain stock model are given. Considering the properties of the American option pricing, the algorithms for computing the expected value of the extreme values based on the Simpson’s rule are designed. Finally, the price fluctuation of the American option is illustrated by numerical experiments.
20 Mar 2023Submitted to Mathematical Methods in the Applied Sciences
20 Mar 2023Assigned to Editor
20 Mar 2023Submission Checks Completed
24 Mar 2023Review(s) Completed, Editorial Evaluation Pending
28 Mar 2023Reviewer(s) Assigned