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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,…
A survey on fractional variational calculus
Ricardo Almeida, Delfim F. M. Torres
Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect…
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…
Optimality conditions for fractional variational problems with free terminal time
Ricardo Almeida
This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional E…
Generalized Fuzzy Euler-Lagrange equations and transversality conditions
O. S. Fard, R. Almeida, J. Soolaki +1
The study of fuzzy fractional variational problems in terms of a fractional Liouville-Caputo derivative is introduced. Necessary optimality conditions for problems of the fuzzy fra…