A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW

Bhawna Pokhriyal; Pranay Goswami; Kranti Kumar

A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW

Abstract

In this paper, a non-standard local fractional Crank-Nicolson finite difference scheme is proposed to determine an approximation to the solutions of the fractal LWR traffic flow model. The scheme is found to be consistent and unconditionally stable. In addition, Lax's equivalence theorem is used to guarantee the scheme's convergence. The suggested approach is validated by discussing a few exemplary cases and associated simulations. The acquired numerical solutions demonstrate how traffic density changes dynamically across time and space. The outcomes obtained with the suggested non-standard finite difference (NSFD) method demonstrate its effectiveness in numerically solving the problem of fractal traffic flow.

Keywords

References

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Details

Primary Language

English

Subjects

Partial Differential Equations

Journal Section

Research Article

Authors

Bhawna Pokhriyal ^*
0009-0000-4868-7049
India

Pranay Goswami
0000-0003-1205-1975
India

Kranti Kumar This is me
0000-0002-6361-8786
India

Publication Date

July 4, 2026

Submission Date

April 15, 2025

Acceptance Date

August 1, 2025

Published in Issue

Year 2026 Volume: 16 Number: 7

IZ

https://izlik.org/JA62ZJ55YA

Cite

RIS / Bibtex

APA

Pokhriyal, B., Goswami, P., & Kumar, K. (2026). A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW. TWMS Journal of Applied and Engineering Mathematics, 16(7), 865-883. https://izlik.org/JA62ZJ55YA

AMA

1.Pokhriyal B, Goswami P, Kumar K. A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW. JAEM. 2026;16(7):865-883. https://izlik.org/JA62ZJ55YA

Chicago

Pokhriyal, Bhawna, Pranay Goswami, and Kranti Kumar. 2026. “A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW”. TWMS Journal of Applied and Engineering Mathematics 16 (7): 865-83. https://izlik.org/JA62ZJ55YA.

EndNote

Pokhriyal B, Goswami P, Kumar K (July 1, 2026) A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW. TWMS Journal of Applied and Engineering Mathematics 16 7 865–883.

IEEE

[1]B. Pokhriyal, P. Goswami, and K. Kumar, “A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW”, JAEM, vol. 16, no. 7, pp. 865–883, July 2026, [Online]. Available: https://izlik.org/JA62ZJ55YA

ISNAD

Pokhriyal, Bhawna - Goswami, Pranay - Kumar, Kranti. “A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW”. TWMS Journal of Applied and Engineering Mathematics 16/7 (July 1, 2026): 865-883. https://izlik.org/JA62ZJ55YA.

JAMA

1.Pokhriyal B, Goswami P, Kumar K. A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW. JAEM. 2026;16:865–883.

MLA

Pokhriyal, Bhawna, et al. “A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 7, July 2026, pp. 865-83, https://izlik.org/JA62ZJ55YA.

Vancouver

1.Bhawna Pokhriyal, Pranay Goswami, Kranti Kumar. A LOCAL FRACTIONAL NON-STANDARD FINITE DIFFERENCE SCHEME FOR FRACTAL LWR MODEL OF TRAFFIC FLOW. JAEM [Internet]. 2026 Jul. 1;16(7):865-83. Available from: https://izlik.org/JA62ZJ55YA