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.
