Narrow Results

In this paper, we introduce and investigate a new class of coupled fractional $q$-integro-difference equations involving Riemann–Liouville fractional $q$-derivatives and $q$-integrals of different orders, equipped with $q$-integral-coupled boundary conditions. The given problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed-points coincide with solutions of the problem at hand. The existence and uniqueness results for the given problem are, respectively, derived by applying Leray–Schauder nonlinear alternative and Banach contraction mapping principle. Illustrative examples for the obtained results are constructed. This paper concludes with some interesting observations and special cases dealing with uncoupled boundary conditions, and non-integral and integral types nonlinearities.

This chapter begins by addressing the food, energy, and water trilemma. A critique of the impact of neoliberalism that traces the transition from industrial to financial capitalism follows. The trade-off arising from improvements in living standards and environmental impact is then explored. In a context where socioeconomic and cultural differences result in conflicting views of what is virtuous, there is a problem of trust. The central proposition is that a new frame grounded in New Institutional Economics (NIE) is required. Fintech and distributed ledger technology (DLT) offer a unique way of building the essential institutional infrastructure required to overcome the problem of trust. Examples showing how fintech can address climate change follow. Whilst these initiatives are to be applauded, new international institutional infrastructure is required to enable fintech to realise its potential. Examples of future possibilities are presented. The chapter concludes by making the case for a new paradigm that prioritises international cooperation because unrestrained competition will lead to rising temperatures, mass migrations, and the collapse of civilisation as we know it.

The problem in defining generalization is considered by examining some core aspects, such as (a) the extent of the domain of validity of a property, (b) the transformation between different non-equivalent representations and (c) the respective representations of different observers and their relationships, i.e., a dynamic theory of relationships between levels of observation as introduced by the Dynamic Usage of Models (DYSAM). The purpose of this paper is to better clarify the conceptual framework of generalization in order to be able to set the context for a General Theory of Emergence as meta-theory, using models of models (as for logical openness) and interacting hierarchies. After considering some approaches used to generalize and focussing upon the purpose of General System Theory for generalizing, we examine some concrete approaches, such as DYSAM, for building up a General Theory of Emergence with specific theories of disciplinary emergence as particular cases.