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In this article, we investigate the existence and uniqueness of the solution of a fractional boundary value problem with conformable fractional derivation of the Caputo-Fabrizio type. In order to study this problem we used a new definition of fractional integral as an inverse of the conformable fractional derivative of Caputo-Fabrizio, therefore, so we transformed the problem to a equivalent linear Volterra-Fredholm integral equations of the second kind, and taking sufficient conditions existence and uniqueness of this solution is proven based on the results obtained. The analytical study is followed by a complete numerical study. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new fractional integral (FI) associated with the Caputo–Fabrizio fractional derivative. As a theoretical example, we have solved a fractional boundary value problem (BVP) using the proposed FI. A Matlab script to solve this BVP is also provided. [ABSTRACT FROM AUTHOR]