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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
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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

Abstract

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 2023Submission Checks Completed
20 Mar 2023Assigned to Editor
24 Mar 2023Review(s) Completed, Editorial Evaluation Pending
28 Mar 2023Reviewer(s) Assigned
30 Jun 2023Editorial Decision: Revise Major
18 Jul 20231st Revision Received
19 Jul 2023Assigned to Editor
19 Jul 2023Submission Checks Completed
19 Jul 2023Review(s) Completed, Editorial Evaluation Pending
20 Jul 2023Reviewer(s) Assigned
17 Sep 2023Editorial Decision: Revise Major
19 Sep 20232nd Revision Received
21 Sep 2023Assigned to Editor
21 Sep 2023Submission Checks Completed
21 Sep 2023Review(s) Completed, Editorial Evaluation Pending
07 Nov 2023Editorial Decision: Accept