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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.

A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense

Khalouta Ali, Kadem Abdelouahab

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 1

43--56

The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.