Open AccessOptimality conditions involving the Mittag–Leffler tempered fractional derivative
Author(s) -
Ricardo Almeida,
Manuel Morgado
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021149
Subject(s) - fractional calculus , discretization , mathematics , generalization , operator (biology) , derivative (finance) , work (physics) , differential operator , calculus (dental) , mathematical optimization , mathematical analysis , physics , medicine , biochemistry , chemistry , dentistry , repressor , transcription factor , economics , gene , thermodynamics , financial economics
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.