This paper addresses the numerical solution of a fractional evolution equation with a weakly singular kernel. The temporal discretization is carried out by the Crank-Nicolson (CN) method based on graded time steps, while the spatial discretization is carried out using an alternating direction implicit (ADI) finite difference method. Stability and convergence rate are also discussed. The convergence rate is O(k2 + h2x + h2y), where k is a parameter of the maximal time steps and hx, hy are the uniform grid steps in space. Three numerical examples are employed to demonstrate the errors and convergence behavior in practice.
In this paper, we establish and analyze a time-stepping second-order compact difference scheme for semilinear Sobolev-type equations with the Riemann-Liouville (R-L) fractional derivative. To address the singularity of the exact solution near the initial time t = 0 caused by the weakly singular kernel, a graded mesh is employed in the time direction. Additionally, a compact difference formula is used for spatial discretization, resulting in a fully discrete scheme with fourth-order spatial convergence. By a novel analytical method suggested by Mustapha (SIAM J Numer Anal 58 (2020) 1319-1338), we then deduce the stability and error estimate of the fully discrete compact difference scheme considering the characteristics of the temporal mesh and suitable regularity assumptions. Numerical examples demonstrate that by selecting the appropriate grading index y, the proposed scheme achieves second-order accuracy in time and fourth-order accuracy in space.
This article is dedicated to the study of fixed/predefined-time stability problem of discontinuous time-varying system. Firstly, based on power function with indefinite time-varying parameter, several novel fixed/predefined-time stability criteria are established via differential inclusion framework. Moreover, a series of estimations of settling-time are provided for fixed-time stability, where their upper bounds are not subject to system’s starting states. Secondly, an interconnected social networks model with multiple subsystems is formulated by considering discontinuous factor and external disturbance. By applying the established fixed/predefined-time stability criteria and formulating suitable input state-feedback control strategies, the fixed/predefined-time stabilization control of interconnected social networks containing discontinuities is achieved. Finally, the numerical simulation experiment is conducted to verify the fixed/predefined-time state-feedback control effects for interconnected social networks.
This paper investigates the effect of CEO overconfidence on corporate financialization and examines whether internal and external governance mechanisms moderate this relationship, using a sample of Chinese A-share listed firms from 2009 to 2019. The results show that firms led by overconfident CEOs exhibit significantly higher levels of financialization. Further analysis indicates that product market competition strengthens the positive influence of CEO overconfidence on financialization, whereas financing constraints weaken it. In contrast, corporate governance quality does not moderate this relationship. These findings deepen the understanding of managerial behavioral drivers of corporate financialization and offer implications for guiding firms toward real-sector investment and reducing financial risk.
The rapid development of digital inclusive finance (DIF) has reshaped financial formats, and corporate charitable activities have thus embraced new opportunities. This study uses data from Chinese A-share listed companies spanning 2011-2023 to explore the impact and mechanism of DIF on corporate charitable donations (CCD). The results reveal that DIF is conducive to promoting CCD. Mechanism tests show that DIF stimulates CCD mainly by relieving financing constraints and reducing information asymmetry. Heterogeneity analysis indicates that the promotional effect of DIF on CCD is more pronounced in underdeveloped regions of traditional finance and for enterprises at the growth stage. Our findings have significant policy implications for guiding financial resources to better serve philanthropy and promote common prosperity.
