Luis M. Camarinha-Matos

Ricardo Almeida

José Oliveira

This book constitutes the refereed proceedings of the 10th IFIP WG 5.5/SOCOLNET Advanced Doctoral Conference on Computing, Electrical and Industrial Systems, DoCEIS 2019, held in Costa de Caparica, Portugal, in May 2019. The 36 revised full papers presented were carefully reviewed and selected from 73 submissions. The papers present selected results produced in engineering doctoral programs and focus on technological innovation for industry and serivce systems. Research results and ongoing work are presented, illustrated and discussed in the following areas: collaborative systems, collaboration and resilient systems, decision and optimization systems, assistive systems, smart environments, smart manufacturing, water monitoring systems, communication systems, and energy systems.

10th IFIP WG 5.5/SOCOLNET Advanced Doctoral Conference on Computing, Electrical and Industrial Systems, DoCEIS 2019, Costa de Caparica, Portugal, May 8–10, 2019, Proceedings

Technological Innovation for Industry and Service Systems

Dina Tavares

Delfim F. M. Torres

​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.

The Variable-Order Fractional Calculus of Variations

The hot pepper notebook. Dotted page journal. Gift idea for people that love hot peppers and cute cartoons.

Ricardo Almeida

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