Controllability Problem of Fractional Neutral Systems: A Survey

The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems

Variation of constant formulas for fractional difference equations

In this paper, we establish variation of constant formulas for both Caputo and Riemann- Liouville fractional difference equations. The main technique is the Z -transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations

Asymptotic properties of discrete linear fractional equations

In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a complete description of the decay to zero of the trajectories of one-dimensional time-invariant stable Caputo and Riemann-Liouville equations. Moreover, we present Volterra convolution equations, that are equivalent to Caputo equations

Доцільність звіту про сукупний дохід для формування дивідендної політики польськими лістинговими компаніями

This study examines the strength and character of relationship between dividend policy and comprehensive income in Polish manufacturing companies. We formulated two research questions:1) does comprehensive income determine the ability to pay out a dividend?2) what is the key role of comprehensive income in shaping a dividend policy?To receive the answers to these questions, we put a research hypothesis stating that in the Polish listed companies a positive relationship between comprehensive income and dividend policy can be observed.The research was conducted among the companies operating in the manufacturing sector (4xx of the Warsaw Stock Exchange (the WSE) classification). The analytical period is between 2009–2017 and reflects the current legal status of the financial reporting of public companies in Poland. Finally, our analysis comprised 83 manufacturing companies and 664 observations.The study procedure was carried out in two stages. The first stage was to show the results of empirical research conducted among the analysed companies and regarding the variability of comprehensive income in comparison to net income (consequently other comprehensive income). At the second stage, we presented the results of investigation on the strength and character of an impact of comprehensive income on dividends. For that purpose, two research methods were used. Firstly, we calculated the Pearson’s correlation coefficients between comprehensive income (and net income) and future dividend ratios, as well as the other company’s performance and tested for significance using the t-Student test. Secondly, we used regression analysis and two one-equation models built for comprehensive income and net income. Moreover, we used descriptive statistics, t- Student test, and F-test.The conducted research allowed us to draw two main conclusions: 1) there was a positive character of dependence between comprehensive income and future dividend, however, the correlation between them was very weak; 2) the impact of comprehensive income on future dividend ratio was positive, but we noted no statistical significance.Дане дослідження вивчає силу та характер взаємозв’язку між дивідендною політикою та сукупним доходом у польських виробничих компаніях. Сформулювано два питання для дослідження: 1) чи визначає сукупний дохід можливість виплачувати дивіденди? 2) яка ключова роль сукупного доходу у формуванні дивідендної політики? Для отримання відповіді на поставлені запитання, нами окреслено гіпотезу дослідження, в якій зазначається, що в польських лістингових компаніях можна спостерігати позитивний взаємозв’язок між сукупним доходом та дивідендною політикою. Дослідження проводилося серед компаній, що працюють у виробничому секторі (4xx класифікації Варшавської фондової біржі (WSE)). Аналітичний період включає 2009–2017 роки та відображає поточний правовий статус фінансової звітності публічних компаній в Польщі. Здійсненим аналізом охоплено 83 виробничі компанії та 664 спостереження. Процедура дослідження проводилась у два етапи. На першому етапі було показано результати емпіричних досліджень, проведених серед проаналізованих компаній і зважаючи на варіабельність сукупного доходу порівняно з чистим доходом (в підсумку – іншим сукупним доходом). На другому етапі було представлено результати дослідження сили та характеру впливу сукупного доходу на дивіденди. З цією метою було використано два методи дослідження. По-перше, було обчислено коефіцієнти кореляції Пірсона між сукупним доходом (та чистим доходом) і майбутніми показниками дивідендів, а також іншими показниками ефективності діяльності компанії, та протестовано на значущість за допомогою тесту t-Student. По-друге, було використано регресійний аналіз та дві однорівневі моделі, побудовані для сукупного доходу та чистого доходу. Більше того, нами використано описову статистику, тест t-Student та F-тест. Проведене дослідження дозволило зробити два основні висновки: 1) існує позитивний характер залежності між сукупним доходом та майбутніми дивідендами, проте співвідношення між ними дуже слабке; 2) вплив сукупного доходу на майбутні показники дивідендів позитивний, але не констатовано статистичної значущості

Schauder’s fixed-point theorem in approximate controllability problems

The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation

Does Short-Termism Influence the Market Value of Companies? Evidence from EU Countries

This paper fits into the stream of current research on the concept of short-termism and its importance for economic sustainability, especially sustainable finance. Short-termism focuses on short time horizons by both corporate managers and the financial markets, and prioritizes short-time shareholder return over the long-term growth of the company’s value. This study engages the short-termism discussion by examining the effect of quarterly reporting on the long-term market value of listed companies. The aim of the article is to determine whether European companies experience the negative effects of short-termism, precisely, whether public companies that prepare quarterly reports, and which focus mainly on achieving the short-term goals of stock exchange investors, are seeing a decline in their market value in the long-term. We have not proven the existence of such a dependence, the increase in reporting frequency of public companies does not contribute to a decline in their long-term market value. In the case of the EU-15 the results of regression model estimation indicate a positive and statistically significant impact of the time of regular quarterly reporting on the buy-and-hold rates of return, in the “new” EU member states this relationship is not observed

8th Conference on Non-integer Order Calculus and Its Applications

This book collects papers from the 8th Conference on Non-Integer Order Calculus and Its Applications that have been held on September 20-21, 2016 in Zakopane, Poland. The preceding two conferences were held in Szczecin, Poland in 2015, and in Opole, Poland, in 2014. This conference provides a platform for academic exchange on the theory and application of fractional calculus between domestic and international universities, research institutes, corporate experts and scholars. The Proceedings of the 8th Conference on Non-Integer Order Calculus and Its Applications 2016 brings together rigorously reviewed contributions from leading international experts. The included papers cover novel various important aspects of mathematical foundations of fractional calculus, modeling and control of fractional systems as well as controllability, detectability, observability and stability problems for this systems