Man-Li Jiao - School of Science, Xi'an University of Architecture and Technology, Xi’an, China
JI-Huan He - National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University,۱۹۹ Ren-Ai Road, Suzhou, China
Chun-Hui He - School of Mathematics, China University of Mining and Technology, Xuzhou ۲۲۱۱۱۶, Jiangsu, P. R. China
Abdulrahman Ali Alsolami - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box ۸۰۲۰۳, Jeddah ۲۱۵۸۹, Saudi Arabia

The variational theory is an inextricable part of both continuum mechanics and physics, and plays an important role in mathematics and nonlinear science, however it is difficult to find a variational formulation for a nonlinear system, and it is more difficult for a fractional differential system. This paper is to search for a variational formulation for the Schrödinger-KdV system with M-fractional derivatives. The fractional complex transformation is used to convert the system into a traditional differential system, and the semi-inverse method is further applied to establish a needed variational principle.

Hamilton principle, fractional calculus, chain rule