Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint.In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined ...Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint.In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of variable fractional order and we present a new variational problem subject to a holonomic constraint. We establish necessary optimality conditions in order to determine the minimizers of the fractional problems. The terminal point in the cost integral,as well as the terminal state, are considered to be free, and we obtain corresponding natural boundary conditions.展开更多
基金supported by Portuguese Funds through the Center for Research and Development in Mathematics and Applications(CIDMA)the Portuguese Foundation for Science and Technology(FCT)(UID/MAT/04106/2013)supported by FCT through the Ph.D. fellowship SFRH/BD/42557/2007
文摘Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint.In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of variable fractional order and we present a new variational problem subject to a holonomic constraint. We establish necessary optimality conditions in order to determine the minimizers of the fractional problems. The terminal point in the cost integral,as well as the terminal state, are considered to be free, and we obtain corresponding natural boundary conditions.
