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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.

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.

The purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing literature review and builds recommendations for potential scholars interested in the subject area.

In this study, the researchers used a systematic literature review procedure to collect data from Scopus. Bibliometric and structured network analyses were used to examine the bibliometric properties of 864 research documents.

As per the findings of the study, publication in the field has been increasing at a rate of 6% on average. This study also includes a list of the most influential and productive researchers, frequently used keywords and primary publications in this subject area. In particular, Thematic map and Sankey’s diagram for conceptual structure and for intellectual structure co-citation analysis and bibliographic coupling were used.

Based on the conclusion presented in this paper, there are several potential implications for research, practice and society.

This study provides useful insights for future research in the area of OPM in financial derivatives. Researchers can focus on impactful authors, significant work and productive countries and identify potential collaborators. The study also highlights the commonly used OPMs and emerging themes like machine learning and deep neural network models, which can inform practitioners about new developments in the field and guide the development of new models to address existing limitations.

The accurate pricing of financial derivatives has significant implications for society, as it can impact the stability of financial markets and the wider economy. The findings of this study, which identify the most commonly used OPMs and emerging themes, can help improve the accuracy of pricing and risk management in the financial derivatives sector, which can ultimately benefit society as a whole.

It is possibly the initial effort to consolidate the literature on calibration on option price by evaluating and analysing alternative OPM applied by researchers to guide future research in the right direction.

In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.

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 paper is to scrutinise the effectiveness of four derivative exchanges’ enforcement efforts since 2007. These exchanges include the Commodity Exchange Inc. and ICE Futures US from the United States and ICE Futures Europe and the London Metal Exchange from the UK.

The paper examines 799 enforcement notices published by four exchanges through a behavioural science lens: HUMANS conceived by Hunt (2023) in Humanizing Rules: Bringing Behavioural Science to Ethics and Compliance.

The paper finds the effectiveness of the exchanges’ enforcement efforts to be a mixed picture as financial markets transition from the digital to artificial intelligence era. Humans remain a key cog in the wheel of market participants’ trading operations, albeit their roles have changed. Despite this, some elements of exchanges’ enforcement regimes have not kept pace with the move from floor to remote trading. However, in other respects, their efforts are or should be, effective, at least in behavioural terms.

The paper’s findings are arguably limited to exchanges based in Anglophone jurisdictions. The information published by the exchanges is variable, making “like-for-like” comparisons difficult in some areas.

The paper makes several recommendations that, if adopted, could help exchanges to increase the potency of their enforcement programmes.

A key aim of the paper is to shift the lens through which the debate concerning the efficacy of exchange-level oversight is conducted. Hitherto, a legal lens has been used, whereas this paper uses a behavioural lens.

Research on strategic alliances is concerned with two issues: continuation and reconfiguration. Building on prior research that examines the two issues separately, the paper studies them simultaneously. This paper aims to investigate how strategic alliances may exert the synergetic effect between dynamics and stability as well as to discuss the dynamic evolution process and influence factors of strategic alliances.

This paper describes the construction of a two-party evolutionary game model of alliance and partners. The model is used to analyze the evolution process of synergetic mechanism to determine when to terminate and when to continue with a partnership. Further, numerical simulation is used to quantify the results and to gain insight into the effects of various factors on the dynamic evolution of the synergetic mechanism.

This paper reveals several synergetic states of dynamics and stability in the alliances. The results show that synergy states are positively affected by the collaborative innovation benefits, alliance management capability, the intensity of intellectual property protection, liquidated damages and reputation losses, and negatively affected by the absorptive capacity of partners.

The study helps the alliance to achieve long-term development as well as to balance the paradoxical relationship. The results suggest that managers of strategic alliances should focus on building strong and long-term relationships in order to achieve high performance innovations. Managers should also pay close attention to their partners’ behaviors in previous alliances.

This paper provides new insights into the paradoxical relationship in alliance by revealing the evolution of synergetic mechanism between dynamics and stability. The results remind alliances to understand the relationship between dynamics and stability and to notice the influence factors of synergistic effects when they are making decisions.

This study aims to systematically review the literature on modern Islamic finance transactions pertaining to Gharar dimensions. Gharar is defined as uncertainty that potentially leads to ambiguities and conflicts in contracts.

The articles reviewed in this study consisted of 13 articles related to Gharar published between 2013 and 2022. All selected articles were empirically and descriptively searched using specific keywords and strings. The main sources for this study were Scopus and Web of Science (WoS), whereas Google Scholar was a supportive database.

The review found that the dimensions that discussed previous research were trying their best to elaborating Gharar in modern financial transactions. They also demonstrate that rigorous study and deployment of the definition remain in the context defined by jurisprudence scholars. The focus of recent studies pertaining to Gharar is derivatives products that indicate high possibility of uncertainty in its operation.

This method relies heavily on the accessed database, namely, Scopus and WoS, also referred to the articles as recommended by the databases. Furthermore, the criteria of inclusion and exclusion of papers outlined by the authors deemed as an intrinsic limitation in writing systematic literature review.

To the best of the authors’ knowledge, this paper is original in its nature whereby the scholars had different comprehension on how Gharar exists in transaction but they still centred in its original meaning of uncertainty. As a result, this paper also realized how Gharar were interpreted differently relied on the contract’s nature and behaviour. In addition, this paper is expected to contribute to understand how Gharar been interpreted in modern finance transactions and finally reached to the point that further research is needed in establishing Gharar parameter for each contract in Islamic commercial law.

The paper attempts to discuss the optimal pricing decisions under the decentralized and centralized decision and analyze the influence of online reviews and in-sale service on dual-channel supply chain. Finally, the authors design a two-part tariff coordination mechanism.

To deal with this pricing conflict problems of dual-channel supply chain consisting of dominant manufacturer and a retailer, considering the fact that online reviews and in-sale service are important factors on consumers’ purchase decisions, the authors establish some basic models and exploit them to discuss the optimal pricing decisions under the decentralized and centralized decision and analyze the influence of online reviews and in-sale service on dual-channel supply chain. Finally, the authors design a profit-sharing coordination mechanism.

The results show that the optimal online direct selling price is positively correlated with product perceived quality obtained from online reviews and negatively correlated with the in-sale service. The traditional retail price is positively correlated with the in-sale service and weakly correlated with online reviews. For the manufacturer and retailer, whether decentralized decision or coordination contract, their profits increase with the increase of the in-sale service in a certain range and quality perceived from spontaneous online reviews. Online reviews and in-sale service are important factors on consumers’ purchase decisions. Positive in-sale services and online reviews can provide consumers with a better shopping experience, thereby promoting their enthusiasm for shopping and improving their quality of life. The two-part tariff coordination mechanism improves the profits of the manufacturer and the traditional retailer, respectively, through the transfer fee.

The proposed approach can well analyze the channel conflicts and pricing problems between retailers and manufacturers with respect to product offline price and online price. The analysis and results can inform decision-making for manufacturers and retailers.

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.