Ricardo M. S. F Almeida Libri

​ 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.

This book discusses the effect of different school building rehabilitation strategies on the classroomsℓ́ℓ indoor environmental quality (IEQ) and presents a multi-objective methodology for school building enclosure optimization combining artificial neural networks and lifecycle costs. The special features of this book are that it (a) presents the state-of-the-art in school building rehabilitation, (b) covers the IEQ assessment of several school buildings, including non-rehabilitated and rehabilitated according to different strategies; and (c) proposes a multi-objective optimization procedure. The rehabilitation of a school building should be regarded as a procedure combining a number of (sometimes conflicting) variables and objectives, including energy, IEQ and costs (initial, operational and maintenance), in the search for an ℓ́ℓoptimum solution.ℓ́ℓ The main benefit of the book is that it discusses the main topics related to school building rehabilitation, presents results of the IEQ assessment on℗ℓ9 school buildings and launches a discussion on how the ℓ́ℓin-useℓ́ℓ performance of schools is key to understanding how designed performance is actually experienced. It maps the most commonly used multi-objective algorithms and artificial neural network architectures and proposes a methodology for combining these numerical tools with dynamic building simulations and lifecycle cost analysis to optimize school building enclosures. This methodology will be of value to scientists and engineers alike, while also addressing a variety of related disciplines, such as civil and mechanical engineering, architecture and mathematics