Herglotz Type Variational Problems on Conformable Calculus

This paper presents generalized Euler-Lagrange equations involving fractional order derivatives for Herglotz type problems. Unlike traditional functionals, the extremals of these problems are derived from differential equations. The fractional generalized Euler-Lagrange equation obtained in this paper includes both the classical generalized Euler-Lagrange equation and the Euler-Lagrange equation obtained for variational problems involving conformable fractional derivatives as special cases. We use this equation to prove the Noether-type theorem for invariant functionals.