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- Title
A CLASS OF FRACTIONAL TWO-POINT BOUNDARY VALUE PROBLEMS: AN ITERATIVE APPROACH.
- Authors
Khuri, S. A.; Sayfy, A.
- Abstract
The current study's goal is to describe and implement a practical numerical solution for addressing a class of two-point nonlinear fractional boundary value problems (FBVP). The fractional differential equations under investigation are complimented with Dirichlet or mixed boundary conditions. The proposed iterative scheme, known as the Green–Picard or Green–Mann iteration approach, is a newly developed method that embeds Green's function into a customized integral operator before applying either Picard's or Mann's iterative procedures. The method converges quickly and with little CPU time, and the scheme's convergence analysis is addressed. To demonstrate the validity and application of the semi-analytical approach, numerical tests were performed on a variety of FBVPs. The numerical findings indicate that the proposed approach has good performance and precision.
- Subjects
BOUNDARY value problems; NONLINEAR boundary value problems; GREEN'S functions; INTEGRAL operators; INTEGRAL functions
- Publication
Journal of Mathematical Sciences, 2024, Vol 280, Issue 1, p84
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-023-06734-1