230 citations · 520 across the 6 of their papers we have counts for
6 papers
The Variable-Order Fractional Calculus of Variations
Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part,…
Combined Fractional Variational Problems of Variable Order and Some Computational Aspects
Dina Tavares, Ricardo Almeida, Delfim F. M. Torres
We study two generalizations of fractional variational problems by considering higher-order derivatives and a state time delay. We prove a higher-order integration by parts formula…
Fractional Herglotz variational problems of variable order
Dina Tavares, Ricardo Almeida, Delfim F. M. Torres
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined…
Constrained fractional variational problems of variable order
Dina Tavares, Ricardo Almeida, Delfim F. M. Torres
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…
Caputo derivatives of fractional variable order: numerical approximations
Dina Tavares, Ricardo Almeida, Delfim F. M. Torres
We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are consid…
Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable Order
Dina Tavares, Ricardo Almeida, Delfim F. M. Torres
We establish necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of variable fractional order. The endpoint of the…