AN EFFICIENT COMPUTATIONAL ALGORITHM BASED ON LEGENDRE POLYNOMIALS FOR FRACTIONAL ORDER SUPPLY CHAIN SYSTEM

Jagdev Singh, Jitendra Kumar (), Devendra Kumar (), Dumitru Baleanu and Obaid Algahtani ()
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Jagdev Singh: Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India†Department of Mathematics, Kyung-Hee University, 26 Kyungheedae-ro, Dongdaeumn-gu, Seoul 02447, Korea
Jitendra Kumar: Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India
Devendra Kumar: ��Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India
Dumitru Baleanu: �Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon¶Institute of Space Sciences-Subsidiary of INFLPR, Magurele-Bucharest, Romania
Obaid Algahtani: ��Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-14

Abstract: Applying an approximate numerical technique to a system of coupled nonlinear ordinary differential equations (ODEs) within a supply chain model is particularly valuable due to its relevance to industrial operations. This paper examines and contrasts two algorithms designed to solve a supply chain model incorporating a control variable and time-fractional derivatives. The first method utilizes the Legendre spectral collocation method (LSCM) combined with Caputo fractional derivatives of arbitrary order. This approach transforms the model into a series of algebraic equations. The second method is based on the fundamental principles of fractional calculus and employs the Newton polynomial interpolation (NPI). Both methods are used to generate numerical solutions for the fractional supply chain model. The effectiveness and accuracy of these computational results are evaluated and compared through various figures and tables presented in the paper.

Keywords: Fractional Order Supply Chain System; Newton Polynomial Interpolation; Legendre Polynomials; Spectral Collocation Method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401073

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