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

Volume 11, Issue 3, pp 428--436 http://dx.doi.org/10.22436/jnsa.011.03.11

Publication Date: February 22, 2018 Submission Date: October 14, 2017 Revision Date: December 17, 2017 Accteptance Date: January 01, 2018

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Authors

Shuqin Zhang - School of Science,, China University of Mining and Technology (Beijing), Beijing 100083, P. R. China. Lei Hu - School of Science, Shandong Jiaotong University, Jinan 250357, Shandong, P. R. China. Sujing Sun - College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, P. R. China.

Abstract

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.

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Keywords

• The Caputo-Fabrizio fractional derivative
• initial value problem
• fractional differential equations
• Banach contraction principle
• uniqueness

MSC

•  26A33
•  34B15

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