Optimality conditions for fractional variational problems with Caputo-Fabrizio fractional derivatives

Advances in Difference Equations

Jianke Zhang¹  Xiaojue Ma²  Lifeng Li³ 

[1] Department of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, China

关键词: fractional variational problems;    optimality conditions;    Caputo-Fabrizio fractional derivative;   

DOI  :  10.1186/s13662-017-1388-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrange function depending on a Caputo-Fabrizio fractional derivative. The new kernel of Caputo-Fabrizio fractional derivative has no singularity, which is critical to interpreting the memory aftermath of the system. This property was not precisely illustrated in the previous definitions. Two special cases of fractional variational problems are considered to demonstrate the application of the optimality conditions.

【 授权许可】

CC BY