The uniqueness of solution for initial value problems for fractional differential equation involving the Caputo-Fabrizio derivative

Zhang, Shuqin ¹ ; Hu, Lei ² ; Sun, Sujing ³

¹ School of Science,, China University of Mining and Technology (Beijing), Beijing 100083, P. R. China
² School of Science, Shandong Jiaotong University, Jinan 250357, Shandong, P. R. China
³ College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, P. R. China

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 3, p. 428-436.

Résumé

In this paper, we study some results about the expression of solutions to some linear differential equations for the Caputo-Fabrizio fractional derivative. Furthermore, by the Banach contraction principle, the unique existence of the solution to an initial value problem for nonlinear differential equation involving the Caputo-Fabrizio fractional derivative is obtained.

Détail

DOI : 10.22436/jnsa.011.03.11

Classification : 26A33, 34B15
Keywords: The Caputo-Fabrizio fractional derivative, initial value problem, fractional differential equations, Banach contraction principle, uniqueness

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