Thai Son Doan, Phan Thi Huong, Peter E. Kloeden
Abstract:
We formulate a \(\theta\)-numerical scheme for solving
Caputo fractional differential equations (Caputo FDEs) of order
\(\alpha\in(0,1)\), with vector fields satisfying a standard
Lipschitz continuity condition in the state variable and a
H\"older continuity condition in the time variable.
The convergence rate is established and a numerical example
is given to illustrate the theoretical results.
The scheme obtained includes the explicit (\(\theta=0\))
and implicit (\(\theta=1\)) counterparts of Euler-like schemes
for Caputo FDEs known in the literature as the Adams-Bashford and
Adams-Moulton schemes, respectively, and essentially linearly
interpolates them.
Submitted August 9, 2024. Published January 9, 2025.
Math Subject Classifications: 34A05, 65L99, 65R20.
Key Words: Caputo fractional differential equations; theta-scheme; Euler scheme;
Adams-Bashford scheme; Adams-Moulton scheme.
DOI: 10.58997/ejde.2025.05
Show me the PDF file (644 KB), TEX file for this article.
 |
Thai Son Doan Institute of Mathematics Vietnam Academy of Science and Technology 18 Hoang Quoc Viet, Ha Noi, Vietnam email: dtson@math.ac.vn |
|---|---|
 |
Phan Thi Huong Department of Mathematics Le Quy Don Technical University 236 Hoang Quoc Viet, Ha Noi, Vietnam email: pthuong175@gmail.com |
 |
Peter E. Kloeden Mathematiches Insitutes Universitat Tubingen D-72076 Tubingen, Germany email: kloeden@math.uni-frankfurt.de |
Return to the EJDE web page