In this article, we are focusing on an extended Calogero–Bogoyavlenskii–Schiff equation which was altered originally from a new generalized fourth-order nonlinear differential equation that obtained from Calogero–Bogoyavlenskii–Schiff equation. We apply simplified Hirota method, which is an exclusive form of the direct Hirota bilinear method, to a specific form of a new generalized fourth-order nonlinear differential equation. The key point in applicability of referred method is attainability proper forms of dispersion relations and phase shifts. Through this procedure, we present different types of solutions for three different cases. We also give constrictions for each solution type in this work so that readers can distinguish differences among types of solutions. In addition, we introduce some graphical representations for obtained solutions, even for existence of complexiton and interaction solutions.
{"title":"Complexiton and interaction solutions to a specific form of extended Calogero–Bogoyavlenskii–Schiff equation via its bilinear form","authors":"Sukri Khareng, Ömer Ünsal","doi":"10.1515/jncds-2024-0029","DOIUrl":"https://doi.org/10.1515/jncds-2024-0029","url":null,"abstract":"\u0000 In this article, we are focusing on an extended Calogero–Bogoyavlenskii–Schiff equation which was altered originally from a new generalized fourth-order nonlinear differential equation that obtained from Calogero–Bogoyavlenskii–Schiff equation. We apply simplified Hirota method, which is an exclusive form of the direct Hirota bilinear method, to a specific form of a new generalized fourth-order nonlinear differential equation. The key point in applicability of referred method is attainability proper forms of dispersion relations and phase shifts. Through this procedure, we present different types of solutions for three different cases. We also give constrictions for each solution type in this work so that readers can distinguish differences among types of solutions. In addition, we introduce some graphical representations for obtained solutions, even for existence of complexiton and interaction solutions.","PeriodicalId":516284,"journal":{"name":"Journal of Nonlinear, Complex and Data Science","volume":"11 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141927446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In marine engineering, optimizing the performance of vessels is a key issue, particularly in increasing fuel efficiency, reducing operating costs, and minimizing environmental impact. One of the most critical determinants of vessel efficiency is hull resistance, which directly affects fuel consumption, power requirements, and cruising speed. We aim to investigate how surface roughness affects hull flow resistance, to quantify the drag variation at different surface roughness levels using special wall functions that reproduce boundary layer dynamics. This approach involves the complex interaction between the intricate complexity of roughness and the nonlinear pressure drag effects on the hull. The KVLCC2 ship model is used as a representative prototype in the CFD analysis based on the RANS equations and the k-omega SST model to independently evaluate the roughness effects on individual ship sections. The comparative analysis with empirical data reveals the complex relationship between surface roughness and ship resistance and provides insights for ship design and operational improvement. The study investigates the interaction between drag coefficient and vessel performance to improve hydrodynamic efficiency.
{"title":"RANS study of surface roughness effects on ship resistance","authors":"Zainab Ali, Gabriella Bognár","doi":"10.1515/jncds-2024-0009","DOIUrl":"https://doi.org/10.1515/jncds-2024-0009","url":null,"abstract":"Abstract In marine engineering, optimizing the performance of vessels is a key issue, particularly in increasing fuel efficiency, reducing operating costs, and minimizing environmental impact. One of the most critical determinants of vessel efficiency is hull resistance, which directly affects fuel consumption, power requirements, and cruising speed. We aim to investigate how surface roughness affects hull flow resistance, to quantify the drag variation at different surface roughness levels using special wall functions that reproduce boundary layer dynamics. This approach involves the complex interaction between the intricate complexity of roughness and the nonlinear pressure drag effects on the hull. The KVLCC2 ship model is used as a representative prototype in the CFD analysis based on the RANS equations and the k-omega SST model to independently evaluate the roughness effects on individual ship sections. The comparative analysis with empirical data reveals the complex relationship between surface roughness and ship resistance and provides insights for ship design and operational improvement. The study investigates the interaction between drag coefficient and vessel performance to improve hydrodynamic efficiency.","PeriodicalId":516284,"journal":{"name":"Journal of Nonlinear, Complex and Data Science","volume":"8 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141335138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we investigate a couple of nonlinear fractional models of eminent interests subsequently the conformable derivative sense is used to designate the fractional order derivatives. The given structures are transformed into nonlinear ordinary differential equations of integer order, and the extended simple equation technique is then employed to solve the resulting equations. Initially, the nonlinear space time fractional Klein–Gordon equation is considered emerging from quantum and classical relativistic mechanics, which have application in plasma physics, dispersive wave phenomena, quantum field theory, and optical fibres. Later, the (2 + 1)-dimensional time fractional Zoomeron equation is analysed which is convenient to explore the innovative phenomena related to boomerons and trappons. As a result, various new soliton solutions are successfully established. The reported results offer a key implementation for analysing the soliton solutions of nonlinear fractional models which are extremely encouraging arising in the recent era of science and engineering. The 3D simulations have been carried out to demonstrate dynamics of the various soliton solutions for a given set of parameters.
{"title":"On the construction of various soliton solutions of two space-time fractional nonlinear models","authors":"K. U. Tariq, Jian-Guo Liu","doi":"10.1515/jncds-2023-0103","DOIUrl":"https://doi.org/10.1515/jncds-2023-0103","url":null,"abstract":"\u0000 In this article, we investigate a couple of nonlinear fractional models of eminent interests subsequently the conformable derivative sense is used to designate the fractional order derivatives. The given structures are transformed into nonlinear ordinary differential equations of integer order, and the extended simple equation technique is then employed to solve the resulting equations. Initially, the nonlinear space time fractional Klein–Gordon equation is considered emerging from quantum and classical relativistic mechanics, which have application in plasma physics, dispersive wave phenomena, quantum field theory, and optical fibres. Later, the (2 + 1)-dimensional time fractional Zoomeron equation is analysed which is convenient to explore the innovative phenomena related to boomerons and trappons. As a result, various new soliton solutions are successfully established. The reported results offer a key implementation for analysing the soliton solutions of nonlinear fractional models which are extremely encouraging arising in the recent era of science and engineering. The 3D simulations have been carried out to demonstrate dynamics of the various soliton solutions for a given set of parameters.","PeriodicalId":516284,"journal":{"name":"Journal of Nonlinear, Complex and Data Science","volume":" 26","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140996253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tuberculosis (TB) is caused by a bacterium called Mycobacterium tuberculosis (Mtb). When Mtb enters inside the pulmonary alveolus, it is phagocytosed by the alveolar macrophages, followed by a cascade of immune responses. This leads to the recruitment and accumulation of additional macrophages and T cells in the pulmonary tissues. A key outcome of this is the formation of granuloma, the hallmark of TB infection. In this paper, we develop a mathematical model of the evolution of granuloma by a system of partial differential equations that is based on the classical Keller–Segel chemotaxis equation. We investigate the effect of different parameters on the formation of granuloma. We present numerical simulation results that illustrate the impact of different parameters. The implication of our result on the disease progression is also discussed.
结核病（TB）是由一种名为结核分枝杆菌（Mtb）的细菌引起的。当 Mtb 进入肺泡内部时，会被肺泡巨噬细胞吞噬，随后产生一系列免疫反应。这导致肺组织中更多巨噬细胞和 T 细胞的招募和聚集。其主要结果是形成肉芽肿，这是肺结核感染的标志。本文以经典的 Keller-Segel 趋化方程为基础，通过偏微分方程系统建立了肉芽肿演变的数学模型。我们研究了不同参数对肉芽肿形成的影响。我们给出了数值模拟结果，以说明不同参数的影响。我们还讨论了我们的结果对疾病进展的影响。
{"title":"A spatial model to understand tuberculosis granuloma formation and its impact on disease progression","authors":"Peng Feng","doi":"10.1515/jncds-2023-0035","DOIUrl":"https://doi.org/10.1515/jncds-2023-0035","url":null,"abstract":"\u0000 Tuberculosis (TB) is caused by a bacterium called Mycobacterium tuberculosis (Mtb). When Mtb enters inside the pulmonary alveolus, it is phagocytosed by the alveolar macrophages, followed by a cascade of immune responses. This leads to the recruitment and accumulation of additional macrophages and T cells in the pulmonary tissues. A key outcome of this is the formation of granuloma, the hallmark of TB infection. In this paper, we develop a mathematical model of the evolution of granuloma by a system of partial differential equations that is based on the classical Keller–Segel chemotaxis equation. We investigate the effect of different parameters on the formation of granuloma. We present numerical simulation results that illustrate the impact of different parameters. The implication of our result on the disease progression is also discussed.","PeriodicalId":516284,"journal":{"name":"Journal of Nonlinear, Complex and Data Science","volume":"25 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140248064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. J. Ouemba Tassé, B. Tsanou, Cletus Kwa Kum, Jean Lubuma
In this paper, we propose a two-group deterministic COVID-19 model which takes into account educational campaigns and the fact that people infected with COVID-19 may choose either modern (allopathic) medicine, traditional medicine or may combine the two modes of treatment. The model is analysed in the case where modern medicine is the only mode of treatment and when traditional medicine is taken as an adjuvant (or another mode of treatment). We prove in the first case that the model has a disease-free equilibrium (DFE), globally asymptotically stable when the control reproduction number is less than one and whenever it is greater than one, we prove the local asymptotic stability of the endemic equilibrium. In the second case, we prove that, misconceptions in the population lead to a backward bifurcation phenomenon, which makes the control of the disease more difficult. We derive using the Lyapunov method that a threshold T $mathcal{T}$ ensures the global asymptotic stability of DFE in some cases when its value is less than one. Both models are fitted using daily COVID-19 cumulative cases reported from January to February 2022 in South Africa. We found a control reproduction number less than one, meaning that COVID-19 will be eliminated. Comparison of the two models fits highlights that misconceptions should be taken into account to accurately describe the dynamics of COVID-19 in South Africa. Numerically, we prove that educational campaigns should focus on preventive measures and both traditional and allopathic medicine health care systems should complement each other in the fight against COVID-19.
{"title":"A mathematical model to study herbal and modern treatments against COVID-19","authors":"A. J. Ouemba Tassé, B. Tsanou, Cletus Kwa Kum, Jean Lubuma","doi":"10.1515/jncds-2023-0062","DOIUrl":"https://doi.org/10.1515/jncds-2023-0062","url":null,"abstract":"\u0000 In this paper, we propose a two-group deterministic COVID-19 model which takes into account educational campaigns and the fact that people infected with COVID-19 may choose either modern (allopathic) medicine, traditional medicine or may combine the two modes of treatment. The model is analysed in the case where modern medicine is the only mode of treatment and when traditional medicine is taken as an adjuvant (or another mode of treatment). We prove in the first case that the model has a disease-free equilibrium (DFE), globally asymptotically stable when the control reproduction number is less than one and whenever it is greater than one, we prove the local asymptotic stability of the endemic equilibrium. In the second case, we prove that, misconceptions in the population lead to a backward bifurcation phenomenon, which makes the control of the disease more difficult. We derive using the Lyapunov method that a threshold \u0000 \u0000 \u0000 T\u0000 \u0000 \u0000$mathcal{T}$\u0000\u0000 \u0000 \u0000 ensures the global asymptotic stability of DFE in some cases when its value is less than one. Both models are fitted using daily COVID-19 cumulative cases reported from January to February 2022 in South Africa. We found a control reproduction number less than one, meaning that COVID-19 will be eliminated. Comparison of the two models fits highlights that misconceptions should be taken into account to accurately describe the dynamics of COVID-19 in South Africa. Numerically, we prove that educational campaigns should focus on preventive measures and both traditional and allopathic medicine health care systems should complement each other in the fight against COVID-19.","PeriodicalId":516284,"journal":{"name":"Journal of Nonlinear, Complex and Data Science","volume":"9 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140253267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article studeis the nonlinear (2 + 1)-dimensional Zoomeron equation by utilizing the various prominent analytical approaches namely the unified method and the extended hyperbolic function approach. The analysis in the current paper demonstrates the presence of travelling wave solutions. The applied methods are utilized as powerful tools to investigate and solve the model. The results obtained through these analytical methods reveal insightful patterns in the behavior of the Zoomeron equation. The significance of our work lies in the uniqueness of the methods employed. The two methods are applied to systematically analyze the equation, revealing hidden patterns and structures within its solution space. This leads to the discovery of a collection of solitary wave solutions such as kink waves, singular kink waves, periodic waves and dark soliton using contour plots, 3D and 2D graphics. In this article, we definitely prove that as the free parameters change, the wave amplitude changes as well. It is shown that the applied strategies are more effective and may be implemented to a variety of contemporary nonlinear evolution models emerging in mathematical physics.
{"title":"Study of explicit travelling wave solutions of nonlinear (2 + 1)-dimensional Zoomeron model in mathematical physics","authors":"K. U. Tariq, Jian-Guo Liu, Sana Nisar","doi":"10.1515/jncds-2023-0068","DOIUrl":"https://doi.org/10.1515/jncds-2023-0068","url":null,"abstract":"\u0000 This article studeis the nonlinear (2 + 1)-dimensional Zoomeron equation by utilizing the various prominent analytical approaches namely the unified method and the extended hyperbolic function approach. The analysis in the current paper demonstrates the presence of travelling wave solutions. The applied methods are utilized as powerful tools to investigate and solve the model. The results obtained through these analytical methods reveal insightful patterns in the behavior of the Zoomeron equation. The significance of our work lies in the uniqueness of the methods employed. The two methods are applied to systematically analyze the equation, revealing hidden patterns and structures within its solution space. This leads to the discovery of a collection of solitary wave solutions such as kink waves, singular kink waves, periodic waves and dark soliton using contour plots, 3D and 2D graphics. In this article, we definitely prove that as the free parameters change, the wave amplitude changes as well. It is shown that the applied strategies are more effective and may be implemented to a variety of contemporary nonlinear evolution models emerging in mathematical physics.","PeriodicalId":516284,"journal":{"name":"Journal of Nonlinear, Complex and Data Science","volume":"50 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140437085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The effect of gravity-field modulation is investigated in a nano liquid-confined Hele-Shaw cell. This study aims to finish the work described in (S. N. Rai, B. S. Bhadauria, K. Anish, and B. K. Singh, “Thermal instability in nanoliquid under four types of magnetic-field modulation within Hele-Shaw cell,” Int. J. Heat Mass Transfer, vol. 145, no. 7, p. 072501, 2023) for oscillatory convection. The existence of the complex Ginzburg-Landau equation (CGLE) model is constrained by the requirement ω2 > 0. The magnetic fluxes in the Hele-shaw cell are governed by CGLE with g-jitter. The quantity of heat-mass transfer is examined in the presence of a g-jitter. In addition, the findings of our research on transport analysis indicate that oscillatory mode is preferable to stationary mode. It is also found that the gravity-driven Hele-Shaw layer has lower transport properties. Further, the transport analysis is compared to previous research and shown to have improved results.
摘要 研究了重力场调制在纳米液体密闭海尔-肖电池中的影响。本研究旨在完成（S. N. Rai, B. S. Bhadauria, K. Anish, and B. K. Singh, "Thermal instability in nanoliquid under four types of magnetic-field modulation within Hele-Shaw cell," Int.J.传热传质，第 145 卷，第 7 期，第 072501 页，2023 年）的振荡对流。复金兹堡-朗道方程（CGLE）模型的存在受限于 ω2 > 0 的要求。研究了存在 g 抖动时的热质传递量。此外，我们的输运分析研究结果表明，振荡模式优于静止模式。研究还发现，重力驱动的 Hele-Shaw 层具有较低的传输特性。此外，我们还将传输分析与之前的研究进行了比较，结果表明传输分析得到了改进。
{"title":"Oscillatory nonlinear thermal instability in nanoliquid under gravity modulation within Hele-Shaw cell","authors":"P. Kiran","doi":"10.1515/jncds-2023-0047","DOIUrl":"https://doi.org/10.1515/jncds-2023-0047","url":null,"abstract":"Abstract The effect of gravity-field modulation is investigated in a nano liquid-confined Hele-Shaw cell. This study aims to finish the work described in (S. N. Rai, B. S. Bhadauria, K. Anish, and B. K. Singh, “Thermal instability in nanoliquid under four types of magnetic-field modulation within Hele-Shaw cell,” Int. J. Heat Mass Transfer, vol. 145, no. 7, p. 072501, 2023) for oscillatory convection. The existence of the complex Ginzburg-Landau equation (CGLE) model is constrained by the requirement ω2 > 0. The magnetic fluxes in the Hele-shaw cell are governed by CGLE with g-jitter. The quantity of heat-mass transfer is examined in the presence of a g-jitter. In addition, the findings of our research on transport analysis indicate that oscillatory mode is preferable to stationary mode. It is also found that the gravity-driven Hele-Shaw layer has lower transport properties. Further, the transport analysis is compared to previous research and shown to have improved results.","PeriodicalId":516284,"journal":{"name":"Journal of Nonlinear, Complex and Data Science","volume":"68 50","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139534726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This study aims to analyze the finite-time stability performance of both non-delayed and delayed fractional-order neural networks. Our primary aim is to investigate the finite-time stability characteristics by introducing a novel inequality designed for estimating the settling time. This fresh inequality serves as the foundation for establishing sufficient criteria, formulated as linear matrix inequalities, which guarantee the finite-time stability of both non-delayed and delayed fractional-order neural networks. Additionally, we underscore the importance of incorporating comprehensive information regarding the lower and upper bounds of the activation function, especially in the context of the proposed non-delayed model. Unlike the previous works, in this paper, the linear matrix inequality technique has been adopted towards the finite-time stability behavior of the proposed model. At last, some numerical examples are examined to validate the efficacy and conservatism of the presented approach and established theoretical results over the existing literature.
{"title":"New LMI constraint-based settling-time estimation for finite-time stability of fractional-order neural networks","authors":"Shafiya Muthu, N. Gnaneswaran","doi":"10.1515/jncds-2023-0020","DOIUrl":"https://doi.org/10.1515/jncds-2023-0020","url":null,"abstract":"Abstract This study aims to analyze the finite-time stability performance of both non-delayed and delayed fractional-order neural networks. Our primary aim is to investigate the finite-time stability characteristics by introducing a novel inequality designed for estimating the settling time. This fresh inequality serves as the foundation for establishing sufficient criteria, formulated as linear matrix inequalities, which guarantee the finite-time stability of both non-delayed and delayed fractional-order neural networks. Additionally, we underscore the importance of incorporating comprehensive information regarding the lower and upper bounds of the activation function, especially in the context of the proposed non-delayed model. Unlike the previous works, in this paper, the linear matrix inequality technique has been adopted towards the finite-time stability behavior of the proposed model. At last, some numerical examples are examined to validate the efficacy and conservatism of the presented approach and established theoretical results over the existing literature.","PeriodicalId":516284,"journal":{"name":"Journal of Nonlinear, Complex and Data Science","volume":"41 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139535074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Aziz El Ghazouani, Fouad Ibrahim Abdou Amir, M. Elomari, Said Melliani
Abstract In this paper, we investigate the existence and uniqueness solutions for a fuzzy Neutral fractional integro-differential equation with non-local conditions. First, we show the existence of solutions with the help of the Non-linear alternative for one-value function, as well as Krasnoselskii’s and Banach’s fixed point theorems. Moreover, we examine the generalized Ulam Hyers (GUH) and Ulam Hyers Rassias stability for our main problem. Finally, an example is presented to show the usability of our major results.
{"title":"Fuzzy neutral fractional integro-differential equation existence and stability results involving the Caputo fractional generalized Hukuhara derivative","authors":"Aziz El Ghazouani, Fouad Ibrahim Abdou Amir, M. Elomari, Said Melliani","doi":"10.1515/jncds-2023-0059","DOIUrl":"https://doi.org/10.1515/jncds-2023-0059","url":null,"abstract":"Abstract In this paper, we investigate the existence and uniqueness solutions for a fuzzy Neutral fractional integro-differential equation with non-local conditions. First, we show the existence of solutions with the help of the Non-linear alternative for one-value function, as well as Krasnoselskii’s and Banach’s fixed point theorems. Moreover, we examine the generalized Ulam Hyers (GUH) and Ulam Hyers Rassias stability for our main problem. Finally, an example is presented to show the usability of our major results.","PeriodicalId":516284,"journal":{"name":"Journal of Nonlinear, Complex and Data Science","volume":"4 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139458458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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