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

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.