A survey on fuzzy fractional variational problems

摘要

This paper focuses on introducing and studying generalized fuzzy Euler–Lagrange equation and fuzzy isoperimetric problem. According to the concept of Caputo-type fuzzy fractional derivative in the sense of the generalized fuzzy differentiability, we extend and establish some definitions on fuzzy fractional calculus of variation and provide some necessary conditions to obtain the fuzzy fractional Euler–Lagrange equation for both constrained and unconstrained fuzzy fractional variational problems. The fuzzy isoperimetric problem is also investigated in relation to the generalized fuzzy Euler–Lagrange. Finally, two examples are given to describe the proposed approach.