Moumen Bekkouche M, Mansouri I, Ahmed A A Azeb
Department of Mathematics, Faculty of Exact Sciences, El Oued University, 39000 El Oued, Algeria.
J Appl Math Comput. 2022;68(6):4305-4316. doi: 10.1007/s12190-022-01708-z. Epub 2022 Feb 4.
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.
在本文中，我们研究了具有Caputo-Fabrizio型一致分数阶导数的分数阶边值问题解的存在性和唯一性。为了研究这个问题，我们使用了一种新的分数阶积分定义，它是Caputo-Fabrizio一致分数阶导数的逆运算，因此，我们将该问题转化为一个等价的第二类线性Volterra-Fredholm积分方程，并根据所得结果证明了该解存在且唯一的充分条件。在进行解析研究之后，我们进行了完整的数值研究。
