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1 Journal of Applied Mathematics and Computational Mechanics

1 2023

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Numerical solution of a fractional coupled system with the Caputo-Fabrizio fractional derivative

Mansouri Ikram, Bekkouche Mohammed Moumen, Ahmed Abdelaziz Azeb

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 1

46--56

Within this work, we discuss the existence of solutions for a coupled system of linear fractional differential equations involving Caputo-Fabrizio fractional orders. We prove the existence and uniqueness of the solution by using the Picard-Lindel ̈of method and fixed point theory. Also, to compute an approximate solution of problem, we utilize the Adomian decomposition method (ADM), as this method provides the solution in the form of a series such that the infinite series converge to the exact solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method.