An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative. (15th March 2021)

• Record Type: Journal Article
• Authors: Marasi, H. R.; Joujehi, A. Soltani; Aydi, H.
• Other Names: Aral Ali Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-03-15
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6624861
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution.