Bernstein polynomials method for solving multi-order fractional neutral pantograph equations with error and stability analysis
Document Type
Article
Source of Publication
Results in Applied Mathematics
Publication Date
5-1-2024
Abstract
In this investigation, we present a new method for addressing fractional neutral pantograph problems, utilizing the Bernstein polynomials method. We obtain solutions for the fractional pantograph equations by employing operational matrices of differentiation, derived from fractional derivatives in the Caputo sense applied to Bernstein polynomials. Error analysis, along with Chebyshev algorithms and interpolation nodes, is employed for solution characterization. Both theoretical and practical stability analyses of the method are provided. Demonstrative examples indicate that our proposed techniques occasionally yield exact solutions. We compare the algorithms using several established analytical methods. Our results reveal that our algorithm, based on Bernstein series solution methods, outperforms others, exhibiting superior performance with higher accuracy orders compared to those obtained from Chebyshev spectral methods, Bernoulli wavelet method, and Spectral Tau method.
DOI Link
ISSN
Publisher
Elsevier BV
Volume
22
Disciplines
Mathematics
Keywords
Bernstein polynomials, Error analysis, Neutral pantograph, Stability analysis
Scopus ID
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Alshbool, M. H.T., "Bernstein polynomials method for solving multi-order fractional neutral pantograph equations with error and stability analysis" (2024). All Works. 6483.
https://zuscholars.zu.ac.ae/works/6483
Indexed in Scopus
yes
Open Access
yes
Open Access Type
Hybrid: This publication is openly available in a subscription-based journal/series