Abstract
In this paper, we deal with the variational problems defined by an integral that include fractional conformable derivative. We obtained the optimality results for variational problems with fixed end-point boundary conditions and variable end-point boundary conditions. Then, we studied on the variational problems with integral constraints and holonomic constraints, respectively.
Highlights
Origin of fractional calculus dates back to 1600’s, ...rstly seen in a letter from Leibnitz to L’Hospital
We deal with the variational problems de...ned by an integral that include fractional conformable derivative
We studied on the variational problems with integral constraints and holonomic constraints, respectively
Summary
Origin of fractional calculus dates back to 1600’s, ...rstly seen in a letter from Leibnitz to L’Hospital. Khalil et al [19] gave a new well-behaved fractional derivative de...nition; named as conformable fractional derivative This new de...nition has many similar properties with ordinary integer order derivative such as constant function rule, linearity, product and quotient rules and Leibnitz rule (see [1]). Conformable fractional derivative, calculus of variations, subsidiary conditions. In order to deal with Lagrangians involving nonconservative forces, Riewe [26] generalized the usual variational methods by using Riemann-Liouville type operators and introduced the fractional order calculus of variations. Agarwal [2, 3, 4] studied variational methods for Riemann-Liouville, Caputo and Riesz fractional derivatives. We consider more general variational problems with conformable fractional derivative and extend the results given in [21]. We investigate variable end-point variational problems and variational problems with subsidiary conditions
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