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In the proposed manuscript, we present a novel mathematical model for analysing the persistence of corruption in human communities, based on fractal-fractional concepts and the Mittag-Leffler kernel law. Corruption is considered analogous to a disease that can spread and influence others who are free from corruption. Our model evaluates the equilibrium points of corruption and tests their stability using the corruption reproduction number. We also apply the fixed point theory concept to check for the existence and uniqueness of a solution, in the context of a fractional fractal operator. Solution stability is verified using the perturbed Ulam Hyers technique, and an approximate solution is obtained through the use of Lagrangian polynomials. To test the validity of our model, we simulate all compartments at different fractional orders and time durations, providing additional insights into the dynamics of corruption beyond natural orders. [ABSTRACT FROM AUTHOR]

In the proposed manuscript, we present a novel mathematical model for analysing the persistence of corruption in human communities, based on fractal-fractional concepts and the Mittag-Leffler kernel law. Corruption is considered analogous to a disease that can spread and influence others who are free from corruption. Our model evaluates the equilibrium points of corruption and tests their stability using the corruption reproduction number. We also apply the fixed point theory concept to check for the existence and uniqueness of a solution, in the context of a fractional fractal operator. Solution stability is verified using the perturbed Ulam Hyers technique, and an approximate solution is obtained through the use of Lagrangian polynomials. To test the validity of our model, we simulate all compartments at different fractional orders and time durations, providing additional insights into the dynamics of corruption beyond natural orders.

Numerous organisations across the globe have significant challenges about corruption, characterised by a systematic, endemic, and pervasive nature that permeates various societal establishments. Hence, we propose the fractional order model of corruption, which encompasses the involvement of corrupt individuals across various stages of education and employment. Specifically, we examine the presence of corruption among children in elementary schools, youths in tertiary institutions, adults in civil services, adults in government and public offices, and individuals who have renounced their involvement in corrupt practices. The basic reproduction number of the system was determined by utilising the next-generation matrix. The strength number was obtained by calculating the second derivative of the corruption-related compartments. The examined model solution’s existence, uniqueness, and stability were established using the Krasnoselski fixed point theorem, the Banach contraction principle, and the Ulam–Hyers theorem, respectively. Based on the numerous figures presented, our simulations indicate a positive correlation between the decline in fractal–fractional order and the increase in the number of individuals susceptible to corruption. This phenomenon results in an increase in the prevalence of corruption among designated sectors of the general population. The persistence of corruption in society is a significant challenge to its eradication, as individuals who see personal gains from engaging in corrupt practices tend to exhibit a recurring inclination towards such behaviour. Nevertheless, it is recommended that to mitigate corruption within various corruption-prone subcategories, there is a need to enhance the level of consciousness and promotion of anti-corruption measures throughout all societal establishments.

This article proposes a nonlinear deterministic mathematical model that encapsulates the dynamics of the prevailing degree of corruption in a population. The objectives are attained by exploring the dynamics of the corruption model under fractional-order derivative in the Caputo sense. The outcomes of the research are facilitated by stratifying the population into five compartments: susceptible class, exposed class, corrupted class, recovered class, and honest class. The developed model is validated by proving pivotal delicacies such as positivity, invariant region, basic reproduction number, and stability analysis. The Ulam–Hyers stability technique is used to prove the stable solution. The Adam–Bashforth numerical scheme is employed to estimate the numerical solution. Moreover, the research environment is further enriched by studying each compartment with respect to a wide range of relevant parametric settings. The realizations of this study indicate that susceptible individuals remain subject to being influenced by corrupt individuals. In addition, it is observed that the population of exposed individuals, recovered individuals, and honest individuals asymptotically approach toward the corruption equilibrium point, whereas the magnitudes of susceptible individuals and corrupted individuals decrease asymptotically to the corruption equilibrium state. The compartment dynamics are witnessed to be sensitive for various fractional-orders indicating the utility of the fractional approach. The findings of this study support the fundamental understanding of conceptualizing corruption in accordance with the viral transmission of infectious disease.

This work examines the issue of tax evasion through underreporting activity. The associated control problem for reducing the number of dishonest citizens and dishonest officers is explicitly analyzed. It is assumed that the social planner can choose the level of effort in order to control the dynamic system through the use of the specific countries' characteristics q and p (the probability of punishing, respectively, a tax-evading citizen and a dishonest officer), and the level of public financial effort represented by taxation τ as control variables. The model implicitly considers that there is a direct correlation between these characteristics and the efficacy and the commitment of the institutional system in contrasting illegality. Hence, in the analysis, p and q are considered as the effective probabilities to be charged the fine. This study supplies a novel approach concerning the dynamic model underlying the optimal control, which is based on the strategic interaction of the economic agents' choices. These latter are described by an evolutionary dynamic process which is strongly characterized by p and q. The analysis supplies a useful policy indication for the social planner in choosing the way to obtain a certain socially desirable target. Moreover, it helps the comprehension of the different corruption and evasion behavior observable in the real world, where countries with similar level of taxation may have different levels of corruption. [ABSTRACT FROM AUTHOR]

Numerous organisations across the globe have significant challenges about corruption, characterised by a systematic, endemic, and pervasive nature that permeates various societal establishments. Hence, we propose the fractional order model of corruption, which encompasses the involvement of corrupt individuals across various stages of education and employment. Specifically, we examine the presence of corruption among children in elementary schools, youths in tertiary institutions, adults in civil services, adults in government and public offices, and individuals who have renounced their involvement in corrupt practices. The basic reproduction number of the system was determined by utilising the next-generation matrix. The strength number was obtained by calculating the second derivative of the corruption-related compartments. The examined model solution's existence, uniqueness, and stability were established using the Krasnoselski fixed point theorem, the Banach contraction principle, and the Ulam–Hyers theorem, respectively. Based on the numerous figures presented, our simulations indicate a positive correlation between the decline in fractal–fractional order and the increase in the number of individuals susceptible to corruption. This phenomenon results in an increase in the prevalence of corruption among designated sectors of the general population. The persistence of corruption in society is a significant challenge to its eradication, as individuals who see personal gains from engaging in corrupt practices tend to exhibit a recurring inclination towards such behaviour. Nevertheless, it is recommended that to mitigate corruption within various corruption-prone subcategories, there is a need to enhance the level of consciousness and promotion of anti-corruption measures throughout all societal establishments. • We propose the fractional order model of corruption. • We examine the presence of corruption among children in elementary schools. • The strength number was obtained by calculating the second derivative of the corruption-related compartments. • The examined model solution's existence, uniqueness, and stability. • Corrupt practices tend to exhibit a recurring inclination towards such behaviour. [ABSTRACT FROM AUTHOR]

Corruption, like cockroaches, has co-existed with human society for a long time. Corruption has received significant attention among economists and international financial institutions during the last few decades, given its implications for economic growth. There is an increasing volume of literature on the relationship between corruption and economic growth, and the general conclusion is that corruption slows down the long-term growth of an economy through a wide range of channels but also that it can have positive or beneficiary effect over economic growth. It hampers economic growth, disproportionately burdens the poor and undermines the effectiveness of investment and aid. Theoretical studies suggest that corruption may counteract government failure and promote economic growth in the short run, given exogenously determined suboptimal bureaucratic rules and regulations. As the government failure is itself a function of corruption, however, corruption should have detrimental effects on economic growth in the long run. In this paper we will analyze and present: First, we will list a number of possible causes and consequences of corruption, derived from a review of the recent empirical and theoretical literature. Second, we will propose a model that can help explain the relationship between corruption and the economic growth. In the third section, we will introduce several measures of corruption, certain empirical correlations and their policy implications, we will then conclude in the last section. [ABSTRACT FROM AUTHOR]