Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

Integrated energy design: education and training in cross-disciplinary teams implementing energy performance of buildings directive (EPBD)

In Europe, energy and climate policies started to take shape from the 1990s onwards culminating with the ambitious 20-20-20 climate goals and the Low-Carbon Europe roadmap 2050. The European Commission empower the importance of achieving the objective of the recast Directive on energy performance of buildings (EPBD) that new buildings built from 2021 onwards will have to be nearly zero-energy buildings. The general belief is that the energy performance optimization of buildings requires an integrated design approach and cross-disciplinary teamwork to optimize the building's energy use and quality of indoor environment while satisfying the occupants' needs.In this context, there is a substantial need for professionals such as architects and engineers specifically trained and educated in integrated design approach and trained to work in cross-disciplinary teams. To be able to push forward the development, it is essential that educational institutions foster professionals with such knowledge, skills and competences. An initiative toward this direction is the EU-project of IDES-EDU: "Master and Post-Graduate education and training in multi-disciplinary teams".The paper describes the necessity of more integrated and cross-disciplinary approaches to building design through state-of-the-art of the building sector and educational initiatives in the participating countries in the project, and through theory of design processes. The paper also communicates the results of newly developed cross-disciplinary education established by fifteen different educational institutions in Europe. Finally, the paper explains and discusses the challenges encountered during development and implementation of the education across different professions and countries. (C) 2013 Elsevier Ltd. All rights reserved.info:eu-repo/semantics/publishedVersio

Variational Problems Involving a Caputo-Type Fractional Derivative

We study calculus of variations problems, where the Lagrange function depends on the Caputo-Katugampola fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo–Hadamard fractional derivatives, with dependence on a real parameter ρ. We present sufficient and necessary conditions of first and second order to determine the extremizers of a functional. The cases of integral and holomonic constraints are also considered

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

What kind of heat loss requirements NZEB and deep renovation sets for building envelope?

In most of countries the energy performance of buildings is defined as (primary) energy use of whole buildingâ s (heating, cooling, ventilation, DHW, lighting, HVAC auxiliary, appliances), not as specific requirements for building envelope. For construction companies of production of modular renovation panels it in necessary to know heat loss properties of building envelope (U, W/(m2â K); ï , W/(mâ K); ï £, W/K; q50, m3/(hâ m2)). In this study it is analyzed what kind of heat loss requirements exists for building envelope to meet on annual basis to following targets: nZEB i.e. national nearly zero energy definition; deep energy renovation with 80 % reduction of primary energy; ZEB i.e. net Zero Energy Building = the annual primary energy use = 0 kWh/(m² a). Indoor climate and energy calculations were made based on national energy calculation methodologies in six countries: Denmark, Estonia, Latvia, Czech Republic, Portugal, and Netherlands. Requirements for heat loss of building envelope vary depending on requirements on indoor climate and energy performance in specific country, outdoor climate, availability of renewable energy, and building typology. The thermal transmittance of the modular wall panels for nZEB was â 5% from pre renovation thermal transmittance in Latvia, â 10% in Estonia and up to 50% in Portugal. For roof the decrease of thermal transmittance was smaller mainly due to smaller thermal transmittance before renovation. Results show the difficulties to reach ZEB with multi-story apartment buildings in cold climate. There are not enough places to install renewables for energy production on site.The study has been conducted in the projects H2020 MoreConnect, TK146 the Estonian Centre of Excellence in Zero Energy and Resource Efficient Smart Buildings and Districts, ZEBE, IUT1−15 Nearly-zero energy solutions and their implementation on deep renovation of buildings