Generalized conformable variational calculus and optimal control problems with variable terminal conditions

Abstract

This paper provides generalized transversality conditions for the problems of variational calculus and optimal control, constructed by the conformable derivative. The generalized term is used to emphasize the problems with performance indexes containing the conformable derivative and defined by the classical integral and to distinguish them from the problems with performance indexes defined by the conformable integral. Special cases of the generalized transversality conditions both for variational calculus and optimal control are exhibited and supported by illustrative examples.

Keywords

• conformable derivative
• fractional order
• optimal control
• variational calculus
• generalized euler-lagrange equation
• generalized transversality condition