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This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.

We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.

Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.

This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.

The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.

In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.

We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.

Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.

Financial mathematics is one of the most rapidly evolving fields in today’s banking and cooperative industries. In the current study, a new fractional differentiation operator with a nonsingular kernel based on the Robotnov fractional exponential function (RFEF) is considered for the Black–Scholes model, which is the most important model in finance. For simulations, homotopy perturbation and the Laplace transform are used and the obtained solutions are expressed in terms of the generalized Mittag-Leffler function (MLF).

The homotopy perturbation method (HPM) with the help of the Laplace transform is presented here to check the behaviours of the solutions of the Black–Scholes model. HPM is well known for its accuracy and simplicity.

In this attempt, the exact solutions to a famous financial market problem, namely, the BS option pricing model, are obtained using homotopy perturbation and the LT method, where the fractional derivative is taken in a new YAC sense. We obtained solutions for each financial market problem in terms of the generalized Mittag-Leffler function.

The Black–Scholes model is presented using a new kind of operator, the Yang-Abdel-Aty-Cattani (YAC) operator. That is a new concept. The revised model is solved using a well-known semi-analytic technique, the homotopy perturbation method (HPM), with the help of the Laplace transform. Also, the obtained solutions are compared with the exact solutions to prove the effectiveness of the proposed work. The different characteristics of the solutions are investigated for different values of fractional-order derivatives.

Given the regional heterogeneity of economic development, electricity consumption in various regions exhibits a discrepant growth pattern. The purpose of this study is to construct a grey system forecasting model with intelligent parameters for predicting provincial electricity consumption in China.

First, parameter optimization and structural expansion are simultaneously integrated into a unified grey system prediction framework, enhancing its adaptive capabilities. Second, by setting the minimum simulation percentage error as the optimization goal, the authors apply the particle swarm optimization (PSO) algorithm to search for the optimal grey generation order and background value coefficient. Third, to assess the performance across diverse power consumption systems, the authors use two electricity consumption cases and select eight other benchmark models to analyze the simulation and prediction errors. Further, the authors conduct simulations and trend predictions using data from all 31 provinces in China, analyzing and predicting the development trends in electricity consumption for each province from 2021 to 2026.

The study identifies significant heterogeneity in the development trends of electricity consumption systems among diverse provinces in China. The grey prediction model, optimized with multiple intelligent parameters, demonstrates superior adaptability and dynamic adjustment capabilities compared to traditional fixed-parameter models. Outperforming benchmark models across various evaluation indicators such as root mean square error (RMSE), average percentage error and Theil’s index, the new model establishes its robustness in predicting electricity system behavior.

Acknowledging the limitations of traditional grey prediction models in capturing diverse growth patterns under fixed-generation orders, single structures and unadjustable background values, this study proposes a fractional grey intelligent prediction model with multiple parameter optimization. By incorporating multiple parameter optimizations and structure expansion, it substantiates the model’s superiority in forecasting provincial electricity consumption.

Traditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.

A novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.

The new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.

This study has positive implications for enriching the method system of multivariable grey prediction model.

This research paper aims to analyze the scientific and grey literature on Quality 4.0 and zero-defect manufacturing (ZDM) frameworks to develop an integrated quality 4.0 framework (IQ4.0F) for quality improvement (QI) based on Six Sigma and machine learning (ML) techniques towards ZDM. The IQ4.0F aims to contribute to the advancement of defect prediction approaches in diverse manufacturing processes. Furthermore, the work enables a comprehensive analysis of process variables influencing product quality with emphasis on the use of supervised and unsupervised ML techniques in Six Sigma’s DMAIC (Define, Measure, Analyze, Improve and Control) cycle stage of “Analyze.”

The research methodology employed a systematic literature review (SLR) based on PRISMA guidelines to develop the integrated framework, followed by a real industrial case study set in the automotive industry to fulfill the objectives of verifying and validating the proposed IQ4.0F with primary data.

This research work demonstrates the value of a “stepwise framework” to facilitate a shift from conventional quality management systems (QMSs) to QMSs 4.0. It uses the IDEF0 modeling methodology and Six Sigma’s DMAIC cycle to structure the steps to be followed to adopt the Quality 4.0 paradigm for QI. It also proves the worth of integrating Six Sigma and ML techniques into the “Analyze” stage of the DMAIC cycle for improving defect prediction in manufacturing processes and supporting problem-solving activities for quality managers.

This research paper introduces a first-of-its-kind Quality 4.0 framework – the IQ4.0F. Each step of the IQ4.0F was verified and validated in an original industrial case study set in the automotive industry. It is the first Quality 4.0 framework, according to the SLR conducted, to utilize the principal component analysis technique as a substitute for “Screening Design” in the Design of Experiments phase and K-means clustering technique for multivariable analysis, identifying process parameters that significantly impact product quality. The proposed IQ4.0F not only empowers decision-makers with the knowledge to launch a Quality 4.0 initiative but also provides quality managers with a systematic problem-solving methodology for quality improvement.

This paper aims to analyse the persistence of the S&P500 and DAX 30 stock indices as well as of the Fed’s Effective Federal Funds rate and of the European Central Bank’s Marginal Lending Facility rate, and the long-run linkages between stock prices and interest rates in the USA and Europe, respectively.

The methodology is based on the concepts of fractional integration and cointegration.

Using monthly data from January 1999 to December 2022, the results can be summarised as follows. All series examined are non-stationary: stock prices are found to be I(1) while interest rates display orders of integration substantially above 1, which implies a rejection of the hypothesis of mean reversion in all cases examined.

This paper uses an appropriate econometric framework to obtain new, reliable empirical evidence. All four series are highly persistent, and mean reversion does not occur in any single case. Moreover, the fractional cointegration analysis suggests that stock prices and interest rates are not linked in the long run.

The present study assesses the commercial bank profit efficiency and its relationship to banking sector competition in a rapidly growing emerging economy, India from 2009 to 2019 using stochastic frontier analysis (SFA).

Lerner indices, conventional and efficiency-adjusted, quantify competition. Two SFA models are employed to calculate alternative profit efficiency (inefficiency) scores: the two-step time-decay approach proposed by Battese and Coelli (1992) and the recently developed single-step pairwise difference estimator (PDE) by Belotti and Ilardi (2018). In the first step of the BC92 framework, profit inefficiency is calculated, and in the second step, Tobit and Fractional Regression Model (FRM) are utilized to evaluate profit inefficiency correlates. PDE concurrently solves the frontier and inefficiency equations using the maximum likelihood process.

The results suggest that foreign banks are less profit efficient than domestic equivalents, supporting the “home-field advantage” hypothesis in India. Further, increasing competition drives bank managers to make riskier lending and investment choices, decreasing bank profit efficiency. However, this effect varies depending on bank ownership and size.

Literature on the competition bank efficiency link is conspicuously scant, with a focus on technical and cost efficiency. Less is known regarding the influence of competition on bank profit efficiency. The article is one of the first to examine commercial bank profit efficiency and its relationship to banking sector competition. Additionally, the study work represents one of the first applications of the FRM presented by Papke and Wooldridge (1996) and the PDE provided by Belotti and Ilardi (2018).

The purpose of this paper is to propose a new grey prediction model, GOFHGM (1,1), which combines generalised fractal derivative and particle swarm optimisation algorithms. The aim is to address the limitations of traditional grey prediction models in order selection and improve prediction accuracy.

The paper introduces the concept of generalised fractal derivative and applies it to the order optimisation of grey prediction models. The particle swarm optimisation algorithm is also adopted to find the optimal combination of orders. Three cases are empirically studied to compare the performance of GOFHGM(1,1) with traditional grey prediction models.

The study finds that the GOFHGM(1,1) model outperforms traditional grey prediction models in terms of prediction accuracy. Evaluation indexes such as mean squared error (MSE) and mean absolute error (MAE) are used to evaluate the model.

The research study may have limitations in terms of the scope and generalisability of the findings. Further research is needed to explore the applicability of GOFHGM(1,1) in different fields and to improve the model’s performance.

The study contributes to the field by introducing a new grey prediction model that combines generalised fractal derivative and particle swarm optimisation algorithms. This integration enhances the accuracy and reliability of grey predictions and strengthens their applicability in various predictive applications.

As an alternative to hiring financial specialists or investment consultants, robo-advisors offer financially automated investment services. This study aims to investigate how robo-advisors' service attributes, risk attitude and financial self-efficacy influence customers' choice preferences of adopting robo-advisors.

Two hundred fifty-one online surveys were used to collect data, and choice-based conjoint analysis was conducted.

Results show that increasing annual fees negatively impact customers' choice preferences. Promotion, general investment education and additional human assistance have a positive impact. Furthermore, risk-seeking and risk-averse customers require more human assistance than risk-neutral customer and customers with high levels of financial self-efficacy prefer more general investment education and additional human assistance than those with lower levels. In addition, customers in the older age group prefer promotion, general investment education and additional human assistance, while wealthy customers prefer lower annual fees, higher general investment education and more additional human assistance compared to middle-class and low-income groups.

This study contributes to robo-advisor providers to provide appropriate service attributes for each customer group.