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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.

This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results.

This paper considered theoretical and numerical methodologies.

This paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures.

The novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.

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.

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.

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.

Achieving a zero-carbon city requires a long-term strategic perspective. The authors propose a decision-making model which would take into account the economic, environmental and social impacts for prioritizing the zero-carbon measures for sustainable urban transportation.

An integrated intuitionistic fuzzy gained and lost dominance score (IF-GLDS) model is introduced based on intuitionistic fuzzy Yager weighted aggregation (IFYWA) operators and proposed weight-determining IF-SPC procedure. In addition, a weighting tool is presented to obtain the weights of decision experts. Further, the feasibility and efficacy of developed IF-SPC-GLDS model is implemented on a multi-criteria investment company selection problem under IFS context.

The results of the developed model, “introducing zero-emission zones” should be considered as the first measure to implement. The preference of this initiative offers sustainable transport in India to achieve a zero-carbon transport by having the greatest impact on the modal shift from cars to sustainable mobility modes with a lower operational and implementation cost as well as having greater public support. The developed model utilized can be relocated to other smart cities which aim to achieve a zero-carbon transport. Sensitivity and comparative analyses are discussed to reveal the robustness of obtained result. The outcomes show the feasibility of the developed methodology which yields second company as the suitable choice, when compared to and validated using the other MCDA methods from the literature, including TOPSIS, COPRAS, WASPAS and CoCoSo with intuitionistic fuzzy information.

A new intuitionistic fuzzy symmetry point of criterion (IF-SPC) approach is presented to find weights of criteria under IFSs setting. Then, an IF-GLDS model is introduced using IFYWA operators to rank the options in the realistic multi-criteria decision analysis (MCDA) procedure. For this purpose, the IFYWA operators and their properties are developed to combine the IFNs. These operators can offer a flexible way to deal with the realistic MCDA problems with IFS context.

The purpose of this manuscript, a state feedback gain depends on the optimal design of fractional order PID controller to time-delay system is established. In established optimal design known as advanced cuttlefish optimizer and random decision forest that is combined performance of random decision forest algorithm (RDFA) and advanced cuttlefish optimizer (ACFO).

The proposed ACFO uses the concept of crossover and mutation operator depend on position upgrading to enhance its search behavior, calculational speed as well as convergence profile at basic cuttlefish optimizer.

Fractional order proportional-integrator-derivative (FOPID) controller, apart from as tuning parameters (kp, ki and kd) it consists of two extra tuning parameters λ and µ. In established technology, the increase of FOPID controller is adjusted to reach needed responses that demonstrated using RDFA theory as well as RDF weight matrices is probable to the help of the ACFO method. The uniqueness of the established method is to decrease the failure of the FOPID controller at greater order time delay method with the help of controller maximize restrictions. The objective of the established method is selected to consider parameters set point as well as achieved parameters of time-delay system.

In the established technique used to evade large order delays as well as reliability restrictions such as small excesses, time resolution, as well as fixed condition defect. These methods is implemented at MATLAB/Simulink platform as well as outcomes compared to various existing methods such as Ziegler-Nichols fit, curve fit, Wang method, regression and invasive weed optimization and linear-quadratic regression method.

This study examines the impact of raising the ceiling value of Electronic Commerce Custom Declarations (ECCD) on Turkey's export performance processed via ECCD during the COVID-19 period.

This paper examines the impact of the pandemic conditions on Cross-Border Electronic Commerce (ECCD) exports from Turkey to 47 countries over 42 months before and during the pandemic. An empirical analysis using the Pooled Mean Group (PMG) and Mean Group (MG), Panel Autoregressive Distributed Lag (ARDL) approach was conducted to identify the factors affecting export flows.

The findings suggest that raising the ceiling of the ECCD trade is a vital factor in increasing exports. and this result is robust after controlling for pandemic conditions. On the other hand, although the COVID-19 shock mitigates the export volume of ECCD in the short run, it changes by reversal and increases the export level in the long run. Additionally, the number of COVID-19 cases and deaths in Turkey have a significant and negative impact on export flows in the short run, while they have a positive and significant effect in the long run.

The results of this study have practical implications for policymakers, emphasizing the potential and significance of Cross-Border E-Commerce (CBEC) trade.

The study is a pioneering effort in the literature of CBEC to explore how changes in the upper limit on customs declarations can affect export flows, taking into account the impact of the COVID-19 pandemic.

Promoting sustainable consumption is key to global sustainable development. The current study aims to explore the impact of environmental risk perception, environmental knowledge, social pressure and health consciousness on sustainable behavior intention among millennial consumers.

This study used a survey method and a self-administered questionnaire to obtain data from the millennial generation. Smart partial least square (PLS) 4.0 was used to analyze data. This research used judgmental sampling and collected 596 valid responses.

The present study indicates that sustainable consumption is becoming more prevalent among millennials. The authors observed that a high level of environmental risk perception, environmental knowledge, social pressure and health consciousness are the antecedents of sustainable behavioral intention, ultimately leading to sustainable consumption behavior.

The current study highlights the millennial generation's sustainable consumption behavior. Researchers, policymakers, scientists, managers, industry professionals and brand managers can use the research findings to establish a sustainable framework.

This research finds that promoting ecological consumption and environmental consciousness can help developing countries achieve environmental sustainability and ecological balance. The research findings add to the literature by offering new insights into customers' pricing perception for sustainable products and sustainable product availability toward sustainable consumption behavior in developing countries.

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.