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1 Journal of Applied Mathematics and Computational Mechanics

1 2020

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Analytical and numerical study for a fractional boundary value problem with a conformable fractional derivative of Caputo and its fractional integral

Bekkouche M. Moumen, Guebbai H.

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 2

31-42

We study the existence and uniqueness of the solution of a fractional boundary value problem with conformable fractional derivation of the Caputo type, which increases the interest of this study. In order to study this problem we have introduced a new definition of fractional integral as an inverse of the conformable fractional derivative of Caputo, therefore, the proofs are based upon the reduction of the problem to a equivalent linear Volterra-Fredholm integral equations of the second kind, and we have built the minimum conditions to obtain the existence and uniqueness of this solution. The analytical study is followed by a complete numerical study.