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In this paper, the fractional calculus (FC) and pseudo-phase space (PPS) techniques are combined for modeling the dynamics of world economies, leading to a new approach for forecasting a country's gross domestic product. In most market economies, the decline of the post-war prosperity brought challenging rivalries to the Western world. Considerable social, political, and military unrest is today spreading in major capital cities of the world. As global troubles including mass migrations and more abound, countries' performance as told by PPS approaches can help to assess national ambitions, commercial aggression, or hegemony in the current global environment. The 1973 oil shock was the turning point for a long-run crisis. A PPS approach to the last five decades (1970-2018) demonstrates that convergence has been the rule. In a sample of 15 countries, Turkey, Russia, Mexico, Brazil, Korea, and South Africa are catching-up to the US, Canada, Japan, Australia, Germany, UK, and France, showing similarity in many respects with these most developed countries. A substitution of the US role as great power in favor of China may still be avoided in the next decades, while India remains in the tail. The embedding of the two mathematical techniques allows a deeper understanding of the fractional dynamics exhibited by the world economies. Additionally, as a byproduct we obtain a foreseeing technique for estimating the future evolution based on the memory of the time series. ; publishersversion ; published

War is a cause of gains and losses. Economic historians have long stressed the extreme importance of considering the economic potential of society for belligerency, the role of management of chaos to bear the costs of battle and casualties, and ingenious and improvisation methodologies for emergency management. However, global and inter-temporal studies on warring are missing. The adoption of computational tools for data processing is a key modeling option with present day resources. In this paper, hierarchical clustering techniques and multidimensional scaling are used as efficient instruments for visualizing and describing military conflicts by electing different metrics to assess their characterizing features: time, time span, number of belligerents, and number of casualties. Moreover, entropy is adopted for measuring war complexity over time. Although wars have been an important topic of analysis in all ages, they have been ignored as a subject of nonlinear dynamics and complex system analysis. This paper seeks to fill these gaps in the literature by proposing a quantitative perspective based on algorithmic strategies. We verify the growing number of events and an explosion in their characteristics. The results have similarities to those exhibited by systems with increasing volatility, or evolving toward chaotic-like behavior. We can question also whether such dynamics follow the second law of thermodynamics since the adopted techniques reflect a system expanding the entropy. ; publishersversion ; published