Using A Linear Programming Method for an Approximate Solution of Linear Fractional Volterra–Fredholm Integro-Differential Equations
DOI:
https://doi.org/10.29304/jqcsm.2025.17.42558Keywords:
Caputo fractional, differential equation, Simplex methodAbstract
This research presents a new algorithm for approximating the linear fractional Volterra-Fredholm integro-differential equation (LFVFIDE) of fractional order α, where (0 < α < 1). The strategy requires that the equation be transformed into a Linear Programming Problem (LPP), allowing the coefficients of the approximate solution to be obtained through an optimization process. The fractional order (α) is depicted in Caputo's sense. Some test examples with exact solutions are solved using the proposed approach, where the results demonstrate the high accuracy and low relative errors of the presented method. Furthermore, different values of α are assigned to each example to enhance the convergence of the proposed technique for fractional-order integro-differential systems.
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Copyright (c) 2025 Samah Mohammed Ali
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