NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL

Ghadah Noman; D. D. Pawar

NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL

Abstract

This paper presents a spectral collocation method based on shifted Vieta-Lucas polynomials (SVLPs) for the numerical approximation of multi-term variable-order fractional differential equations (MT-VOFDEs) involving the Atangana-Baleanu-Caputo (ABC) fractional derivative in variable-order form. A novel operational matrix of the ABC derivative is derived in the SVLP framework, enabling an efficient transformation of the fractional system into an algebraic system. The stability and convergence of the method are theoretically analyzed. The proposed SVLP-based approach is then applied to several test problems, including systems of MT-VOFDEs with known exact polynomial solutions. Numerical results demonstrate exponential convergence, high accuracy, and reduced computational cost compared to other polynomial-based collocation methods. The orthogonality and recursive structure of the SVLPs contribute to computational efficiency and robustness. These findings highlight the effectiveness of the proposed method for solving complex fractional models governed by non-singular kernel operators.

Keywords

References

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Details

Primary Language

English

Subjects

Numerical Analysis, Lie Groups, Harmonic and Fourier Analysis, Real and Complex Functions (Incl. Several Variables)

Journal Section

Research Article

Authors

Ghadah Noman ^*
0009-0002-2763-7637
Yemen

D. D. Pawar
0000-0001-8986-5243
India

Publication Date

August 7, 2026

Submission Date

May 23, 2025

Acceptance Date

September 24, 2025

Published in Issue

Year 2026 Volume: 16 Number: 8

IZ

https://izlik.org/JA72XF28WR

Cite

RIS / Bibtex

APA

Noman, G., & Pawar, D. D. (2026). NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL. TWMS Journal of Applied and Engineering Mathematics, 16(8), 1018-1034. https://izlik.org/JA72XF28WR

AMA

1.Noman G, Pawar DD. NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL. JAEM. 2026;16(8):1018-1034. https://izlik.org/JA72XF28WR

Chicago

Noman, Ghadah, and D. D. Pawar. 2026. “NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL”. TWMS Journal of Applied and Engineering Mathematics 16 (8): 1018-34. https://izlik.org/JA72XF28WR.

EndNote

Noman G, Pawar DD (August 1, 2026) NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL. TWMS Journal of Applied and Engineering Mathematics 16 8 1018–1034.

IEEE

[1]G. Noman and D. D. Pawar, “NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL”, JAEM, vol. 16, no. 8, pp. 1018–1034, Aug. 2026, [Online]. Available: https://izlik.org/JA72XF28WR

ISNAD

Noman, Ghadah - Pawar, D. D. “NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL”. TWMS Journal of Applied and Engineering Mathematics 16/8 (August 1, 2026): 1018-1034. https://izlik.org/JA72XF28WR.

JAMA

1.Noman G, Pawar DD. NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL. JAEM. 2026;16:1018–1034.

MLA

Noman, Ghadah, and D. D. Pawar. “NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 8, Aug. 2026, pp. 1018-34, https://izlik.org/JA72XF28WR.

Vancouver

1.Ghadah Noman, D. D. Pawar. NUMERICAL APPROXIMATION OF ABC-TYPE FRACTIONAL EQUATIONS USING A VIETA-LUCAS POLYNOMIAL. JAEM [Internet]. 2026 Aug. 1;16(8):1018-34. Available from: https://izlik.org/JA72XF28WR