Numerical solution of fractional boundary value problem with caputo-fabrizio and its fractional integral

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.

Automated summary

In this article, we investigate the existence and uniqueness of the solution of a fractional boundary value problem with a specific type of conformable fractional derivation. By using a new definition of fractional integral, we transform the problem into an equivalent linear Volterra-Fredholm integral equation, and based on the results obtained, we prove the sufficient conditions for the existence and uniqueness of the solution. Additionally, a comprehensive numerical study is conducted.