NUMERICAL SOLUTIONS OF MULTI-TERM VARIABLE ORDER FRACTIONAL DIFFERENTIAL EQUATION BASED ON LEGENDRE POLYNOMIALS

Bin Xu; Yingchao Zhang

doi:10.11948/20250347

2026 Volume 16 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2026 > 16(6): 3320-3336

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Bin Xu, Yingchao Zhang. NUMERICAL SOLUTIONS OF MULTI-TERM VARIABLE ORDER FRACTIONAL DIFFERENTIAL EQUATION BASED ON LEGENDRE POLYNOMIALS[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 3320-3336. doi: 10.11948/20250347

Citation:

Bin Xu, Yingchao Zhang. NUMERICAL SOLUTIONS OF MULTI-TERM VARIABLE ORDER FRACTIONAL DIFFERENTIAL EQUATION BASED ON LEGENDRE POLYNOMIALS[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 3320-3336. doi: 10.11948/20250347

NUMERICAL SOLUTIONS OF MULTI-TERM VARIABLE ORDER FRACTIONAL DIFFERENTIAL EQUATION BASED ON LEGENDRE POLYNOMIALS

Bin Xu^1,,
Yingchao Zhang^2, ,

1.
AVIC General Huanan Aircraft Industry CO., LTD, 519060 Zhuhai, China
2.
Zhuhai College of Science and Technology, 519040 Zhuhai, China

Author Bio: Email: 1170726820@qq.com(B. Xu)
Corresponding author: Email: zhych0314@163.com(Y. Zhang)

Abstract

Abstract

This paper proposes a novel framework for the numerical solution of multi-term variable-order fractional differential equations. By leveraging the properties of Legendre polynomials, we construct an orthonormal basis within a reproducing kernel space, which facilitates the formulation of an efficient $ {\varepsilon}- $approximate solution. The algorithm's robustness is underpinned by a rigorous convergence analysis, and its computational efficiency and high accuracy are further substantiated through three illustrative numerical examples.
- Multi-term constant order fractional differential equation /
- convergence /
- Legendre polynomials /
- ε−approximation solution
MSC: 65L10, 34A08, 26A33

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References

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