A Morgan-Voyce Polynomial Framework for Solving Variable-Order Atangana–Baleanu Fractional Differential Equations

Ghadah S. E. Noman and D. D. Pawar

International Journal of Differential Equations, 2026, vol. 2026, 1-15

Abstract: This paper presents a novel and efficient spectral collocation framework for solving nonlinear variable-order fractional differential equations (VO-FDEs) involving the Atangana–Baleanu–Caputo (ABC) operator. Shifted Morgan-Voyce polynomials (SMVPs) are employed as basic functions to construct a new operational matrix specifically adapted to the variable-order ABC operator. This matrix substantially reduces computational complexity while maintaining high accuracy. The proposed approach converts VO-FDEs into tractable nonlinear algebraic systems. In contrast to existing polynomial-based techniques, the framework demonstrates enhanced robustness in handling nonlinearities and variable memory effects, delivering superior precision and stability. Numerical experiments are conducted on challenging nonlinear and multiterm VO-FDEs. Comparative analyses confirm the advantages of the Morgan–Voyce polynomials (MVPs)-based scheme over classical spectral methods. These findings establish the proposed method as a versatile and reliable tool for tackling complex VO-FDEs with nonsingular memory kernels.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ijde/2026/5844250.pdf (application/pdf)
http://downloads.hindawi.com/journals/ijde/2026/5844250.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:5844250

DOI: 10.1155/ijde/5844250

Access Statistics for this article

More articles in International Journal of Differential Equations from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().