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Under suitable continuity and uniqueness conditions, solutions of an α order Caputo fractional boundary value problem are differentiated with respect to boundary values and boundary points. This extends well-known results for nth order boundary value problems. The approach used applies a standard algorithm to achieve the result and makes heavy use of recent results for differentiation of solutions of Caputo fractional intial value problems with respect to initial conditions and continuous dependence for Caputo fractional boundary value problems.

This paper investigates the existence and nonexistence of positive solutions for a class of nonlinear Riemann–Liouville fractional boundary value problems of order α+2n, where α∈(m−1,m] with m≥3 and m,n∈N. The conjugate fractional boundary conditions are inspired by Lidstone conditions. The nonlinearity depends on a positive parameter on which we identify constraints that determine the existence or nonexistence of positive solutions. Our method involves constructing Green’s function by convolving the Green functions of a lower-order fractional boundary value problem and a conjugate boundary value problem and using properties of this Green function to apply the Guo–Krasnosel’skii fixed-point theorem. Illustrative examples are provided to demonstrate existence and nonexistence intervals.

Due to the restrictive growth and/or monotonicity requirements inherent in their employment, classical iterative fixed-point theorems are rarely used to approximate solutions to an integral operator with Green’s function kernel whose fixed points are solutions of a boundary value problem. In this paper, we show how one can decompose a fixed-point problem into multiple fixed-point problems that one can easily iterate to approximate a solution of a differential equation satisfying one boundary condition, then apply a bisection method in an intermediate value theorem argument to meet a second boundary condition. Error estimates on the iterates are also established. The technique will be illustrated on a second-order right focal boundary value problem, with an example provided showing how to apply the results.

How do competing social influences shape individual partisanship over the course of the life cycle? People enter and exit a host of environments over the course of the lifespan, and these environments provide social pressures that can conflict or reinforce early socialized attitudes. Socialization could be an agent for either opinion change or opinion stability. Using the Youth-Parent Socialization Study and constructing partisan environmental measures at the county level, I explore this question. The findings demonstrate that environments exert significant socializing influence over the lifespan, moderating the persistence of early forces. This helps us understand when early socialized pressures persist and when they do not. When environments throughout life provide reinforcing social pressures, parental influence endures over time. However, when early socialized influence is challenged over time by the political environment that citizens reside in, the influence of early parental socialization is offset and nullified.

In this paper, we employ Krasnoseľskii’s fixed point theorem to show the existence of positive solutions to three different two point fractional boundary value problems with fractional boundary conditions. Also, nonexistence results are given.

Do citizens have the information they need to hold state politicians accountable? We consider what people know about state politics and whether knowledge of state government is rooted in the same factors that explain knowledge of national matters.We argue that while knowledge of national politics is rooted within individual dispositions like education and political interest, knowledge of state politics depends on the political climate of the state. When state political environments provide more information and greater incentives to become informed, people are more knowledgeable about state matters. Even if citizens are not always well versed in matters of state politics, they appear to monitor the business of the states. Citizens are most knowledgeable about state politics in the cases where information is arguably most important—when state governments are underperforming, when political competition is high, and when the political parties in the state are ideologically divided.

Questions of whether to enforce COVID-related mask mandates are complex. While enforced mandates are more effective at controlling community spread, government imposed behavioral controls have met significant opposition in conservative states, where a political bloc on the right is skeptical that COVID presents a significant and immediate threat. The authors conduct a split sample survey in order to examine how inclusion of a fine provision attached to mask mandates affects support. The survey was conducted in Idaho (a Republican dominated state) at a time when a mask mandate was a central debate. Unsurprisingly, respondents were more supportive of a mask mandate if a fine was not included. Further investigation indicates this is primarily a result of shifting Republican attitudes, which highlights the complex political situation in conservative states as leaders consider best mechanisms for battling COVID.

Drawing on the sizable literature on polarization in the American public, we consider the link between discussion network composition and perceptions of polarization. Participants in the 2008–2009 ANES panel study were asked to complete an innovative battery; they interactively moved histograms to rate other groups’ positions on several prominent issues. These novel exercises provide data on individuals’ projections of the average attitudes of others, but critically, they also provide data on the variability of such attitudes. Thus, we use these “responsedistributions” to thoroughly assess (1) the relationship between network characteristics and perceptions of the distance between party opinions, and (2) the relationship between network characteristics and perceptions of the homogeneity of opinions within parties. We find evidence that discussion networks track with individual perceptions of the parties in the electorate: exposure to interpersonal disagreement predicts the perception of less distance between (the mean opinions of) the parties, and the reporting of more heterogeneity of opinion within the parties. We conclude by discussing the implications of these findings for democratic functioning more generally.

Interpersonal disagreement has been linked to a variety of democratic outcomes, and classic theories of social influence place it at the heart of opinion formation. We examine the relationship between exposure to disagreement and information seeking during elections, while developing and testing a theory of heterogeneous effects based on recent work on personality and discussion (e.g., Gerber et al. 2012). Using a simulated campaign experiment (Lau and Redlawsk 2006) and data from the 2008–9 ANES panel study, we find consistent evidence that personality conditions responses to disagreement in expected ways—it enhances effects for those with certain traits, while suppressing it for those with others. We close by reflecting on this pattern of results, discussing broader implications while moving toward a more general theory of social influence.

How do people assign blame in the wake of significant government failures? If the role of the citizenry in a representative democracy is to discipline elected officials for failing to meet collective expectations, then this question is of paramount importance. Much research suggests that the base tendency of citizens is to simply blame the other party—a normatively concerning outcome. However, some argue that information, especially that from expert and nonpartisan sources, may push citizens to overlook their party affiliation and assign blame in a more performance-based fashion. Using an experimental design, we test this possibility, manipulating whether there is unified or divided government, the partisanship of key actors, and the nature of expert information that participants receive during a hypothetical budget crisis at the state level. We find strong evidence that party weighs heavily on individuals' minds when assigning blame, as expected. More importantly, we find that nonpartisan expert information about the situation does not live up to its potential to sway partisans from their priors. Rather, unbiased information appears to be used as a weapon— ignored when it challenges partisan expectations and used to magnify blame of the other party when it conforms with them.