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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations
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The Variable-Order Fractional Calculus of Variations (Paperback, 1st ed. 2019)
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The Variable-Order Fractional Calculus of Variations (Paperback, 1st ed. 2019)
Series: SpringerBriefs in Applied Sciences and Technology
Expected to ship within 10 - 15 working days
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The Variable-Order Fractional Calculus of Variations is devoted to
the study of fractional operators with variable order and, in
particular, variational problems involving variable-order
operators. This brief presents a new numerical tool for the
solution of differential equations involving Caputo derivatives of
fractional variable order. Three Caputo-type fractional operators
are considered, and for each one, an approximation formula is
obtained in terms of standard (integer-order) derivatives only.
Estimations for the error of the approximations are also provided.
The contributors consider variational problems that may be subject
to one or more constraints, where the functional depends on a
combined Caputo derivative of variable fractional order. In
particular, they establish necessary optimality conditions of
Euler-Lagrange type. As the terminal point in the cost integral is
free, as is the terminal state, transversality conditions are also
obtained. The Variable-Order Fractional Calculus of Variations is a
valuable source of information for researchers in mathematics,
physics, engineering, control and optimization; it provides both
analytical and numerical methods to deal with variational problems.
It is also of interest to academics and postgraduates in these
fields, as it solves multiple variational problems subject to one
or more constraints in a single brief.
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