Optimality conditions involving the Mittag–Leffler tempered fractional derivative

Abstract

<p style='text-indent:20px;'>In this work we study problems of the calculus of the variations, where the differential operator is a generalization of the tempered fractional derivative. Different types of necessary conditions required to determine the optimal curves are proved. Problems with additional constraints are also studied. A numerical method is presented, based on discretization of the variational problem. Through several examples, we show the efficiency of the method.</p>