The Variable-Order Fractional Calculus of Variations

This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter 1) and of the fractional calculus of variations (Chapter 2). In Chapter 1, we start with a brief overview about fractional calculus and an introduction to the theory of some special functions in fractional calculus. Then, we recall several fractional operators (integrals and derivatives) definitions and some properties of the considered fractional derivatives and integrals are introduced. In the end of this chapter, we review integration by parts formulas for different operators. Chapter 2 presents a short introduction to the classical calculus of variations and review different variational problems, like the isoperimetric problems or problems with variable endpoints. In the end of this chapter, we introduce the theory of the fractional calculus of variations and some fractional variational problems with variable-order. In the second part, we systematize some new recent results on variable-order fractional calculus of (Tavares, Almeida and Torres, 2015, 2016, 2017, 2018). In Chapter 3, considering three types of fractional Caputo derivatives of variable-order, we present new approximation formulas for those fractional derivatives and prove upper bound formulas for the errors. In Chapter 4, we introduce the combined Caputo fractional derivative of variable-order and corresponding higher-order operators. Some properties are also given. Then, we prove fractional Euler-Lagrange equations for several types of fractional problems of the calculus of variations, with or without constraints.Comment: The final authenticated version of this preprint is available online as a SpringerBrief in Applied Sciences and Technology at [https://doi.org/10.1007/978-3-319-94006-9]. In this version some typos, detected by the authors while reading the galley proofs, were corrected, SpringerBriefs in Applied Sciences and Technology, Springer, Cham, 201

Evaluation of policy alternatives to reduce alcohol-related traffic fatalities

This paper reviews the alternative policies to reduce traffic fatalities due to drunk-driving presented in the literature and elaborates on their contradictions to develop a larger, more encompassing program of research to evaluate the effective results of these alternatives when implemented across states and over time. The goals of this research are both societal and scientific. Five major types of policies are generally presented to accomplish the reduction of alcohol-related fatalities: deterrence policies, alcohol policies, transportation policies, education and rehabilitation policies, and civil liability policies. The literature review on alcohol-related traffic fatalities reveals a large number of studies developed in this area, not always with consensual results. One important idea to retain is that the units of analysis, methods, and data are extremely diverse, which makes any attempt to provide a comprehensive set of policies to solve the problem an extremely complex task.Fundação para a Ciência e Tecnologia (FCT

Can the market be used to preserve land? the case for transfer of development rights

This paper discusses the use of a market-driven technique – transfer of development rights (TDR) – to preserve land from development while guaranteeing the rights of property owners. While the technique is often used in the United States, Europe has a lot more urgency in land preservation but it is still lagging in the use of market based instruments such as the transfer of development rights. This paper explores the economic arguments favoring the use of TDR programs, discusses the difficulties in implementing these programs in Europe, where command-and-control regulation has been preferred in land preservation to market-based solutions, and presents tentative hypotheses to explain the adoption of TDR programs in local communities. Preliminary data collected for TDR programs in Florida supports some of the arguments presented and encourages researchers to extend this empirical analysis to European countries

Look what the cat dragged in : national responses to the EU packaging and packaging waste directive

In 1994, the European Union approved the Packaging and Packaging Waste Directive (Directive 94/62/EC) having as a primary goal to mandate the adoption of national legislation targeted at the increase of recovery and recycling goals by member States. In spite of the flexibility allowed by the EU in choosing the path towards goal attainment, a significant number of countries adopted voluntary agreements generally known as Green-Dot consortia. The main research question reflects this concern over the dominant governance structure adopted, the Green Dot agreements: Did voluntary agreements improve the performance of national recycling systems or did they favour collusion practices that dominate the industry, impose barriers to entry by new firms, and generate social welfare losses? The paper discusses the alternative governance structures to manage packaging waste (command-and-control regulation, market-based instruments, and voluntary agreements) and focuses on the economic transaction costs entailed by each of these alternative solutions. It is stressed that proper institutional design is crucial in order to minimize these transaction costs and improve the degree of efficiency of these governance structures

Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure

Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation function at a given height, the mean height of the upper surface for a given number of deposited particles and the interfacial width at a given height. Evidences are given that the fractal dimension of the deposits remains constant as the deposition proceeds, independently of the dipolar strength. These same deposits are used to obtain the growth probability measure through Monte Carlo techniques. It is found that the distribution of growth probabilities obeys multifractal scaling, i.e. it can be analyzed in terms of its $f(\alpha)$ multifractal spectrum. For low dipolar strengths, the $f(\alpha)$ spectrum is similar to that of diffusion-limited aggregation. Our results suggest that for increasing dipolar strength both the minimal local growth exponent $\alpha_{min}$ and the information dimension $D_1$ decrease, while the fractal dimension remains the same.Comment: 10 pages, 7 figure

Institutions, incentives, and the politics of growth management

Paper prepared for the Florida Political Science Association meeting March 23-24, 2001 Jacksonville, FLLand use management is relevant to the discussion of environmental policy because regulation of land use and growth has been used as an instrument of environmentally concerned actors. More generally, growth management policy is best characterized as regulatory, because state and local governments use public policy to direct private behavior (Feiock, 1994). It is appropriate to note however that, the consequences of growth management are inherently distributive. Molotch (1976) depicted a city as an aggregate of competing land-based interests. Decisions regarding growth, at the local or any other level, are then decisions of who gets what, where, and how (Lasswell, 1936). These interests refer not only to competition for economic development but also for quality of life under the heading of growth management. In this discussion of land use management policy, I proceed in the following manner. First, I begin by describing the history and evolution of American land use planning activities and policies throughout the XX century. Next, I succinctly describe the land use policy tools employed over the years and the context in which they have been used. In the core of the paper, I apply a transaction cost theory to explain the relationship between states and localities in terms of economic and political transaction costs. I conclude with some suggestions regarding hypothesis and future theory testing