Sombir Dhaniya, Anoop Kumar, Aziz Khan, T. Abdeljawad, Manar A. Alqudah
In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. The results presented in this study establish the existence, uniqueness, and Hyers–Ulam (HU) stability of the solution to the proposed equation. We achieved our main result by using the Banach contraction mapping principle and Krasonoselskii’s fixed point theorem. Furthermore, we introduce an application to demonstrate the validity of the results of our findings.
{"title":"Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator","authors":"Sombir Dhaniya, Anoop Kumar, Aziz Khan, T. Abdeljawad, Manar A. Alqudah","doi":"10.1155/2023/2288477","DOIUrl":"https://doi.org/10.1155/2023/2288477","url":null,"abstract":"In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. The results presented in this study establish the existence, uniqueness, and Hyers–Ulam (HU) stability of the solution to the proposed equation. We achieved our main result by using the Banach contraction mapping principle and Krasonoselskii’s fixed point theorem. Furthermore, we introduce an application to demonstrate the validity of the results of our findings.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"307 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77511770","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}
<jats:p>The relay fusion frame proposed by Hong and Li is an extension of a fusion frame that has many applications in science. In this study, we introduce relay fusion frames in Hilbert <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <msup> <mrow> <mi>C</mi> </mrow> <mi>∗</mi> </msup> </math> </jats:inline-formula>-modules very naturally and shift some common attributes of fusion frames and relay fusion frames in Hilbert spaces to relay fusion frames in Hilbert <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <msup> <mrow> <mi>C</mi> </mrow> <mi>∗</mi> </msup> </math> </jats:inline-formula>-modules. In addition, we generalize some perturbation results in frame theory to relay fusion frames in Hilbert <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <msup> <mrow> <mi>C</mi> </mrow> <mi>∗</mi> </msup> </math> </jats:inline-formula>-modules. Finally, we introduce a class of <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"> <mfenced open="(" close=")" separators="|"> <mrow> <mi>F</mi> <mo>,</mo> <mi>G</mi> </mrow> </mfenced> </math> </jats:inline-formula>-relay fusion frames as a generalization of <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M7"> <mi>K</mi> </math> </jats:inline-formula>-frames and present some perturbation results for <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M8"> <mfenced open="(" close=")" separators="|"> <mrow> <mi>F</mi> <mo>,</mo> <mi>G</mi> </mrow> </mfenced> </math> </jats:inline-formula>-relay fusion frames in Hilbert <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M9">
Hong和Li提出的中继融合框架是对融合框架的扩展，在科学上有许多应用。在这项研究中，我们很自然地在Hilbert C *模中引入了继电融合框架，并将Hilbert空间中的融合框架和继电融合框架的一些共同属性转移到Hilbert空间中的继电融合框架C * -模。此外，我们将框架理论中的一些微扰结果推广到Hilbert C * -模中的中继融合框架。最后，我们引入一类F，G -中继融合帧作为K -帧的推广，并给出了F的一些摄动结果。Hilbert C *模中的G -继电器熔合帧。
{"title":"Some Generalizations of Relay Fusion Frames and <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mo>,</mo>\u0000 ","authors":"Xiujiao Chi, G. Hong, Pengtong Li","doi":"10.1155/2023/5920210","DOIUrl":"https://doi.org/10.1155/2023/5920210","url":null,"abstract":"<jats:p>The relay fusion frame proposed by Hong and Li is an extension of a fusion frame that has many applications in science. In this study, we introduce relay fusion frames in Hilbert <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mi>∗</mi>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>-modules very naturally and shift some common attributes of fusion frames and relay fusion frames in Hilbert spaces to relay fusion frames in Hilbert <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mi>∗</mi>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>-modules. In addition, we generalize some perturbation results in frame theory to relay fusion frames in Hilbert <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mi>∗</mi>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>-modules. Finally, we introduce a class of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mo>,</mo>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>-relay fusion frames as a generalization of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <mi>K</mi>\u0000 </math>\u0000 </jats:inline-formula>-frames and present some perturbation results for <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mo>,</mo>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>-relay fusion frames in Hilbert <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\">\u0000 ","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"109 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79595769","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}
W. Afzal, K. Shabbir, M. Arshad, Joshua Kiddy K. Asamoah, A. Galal
<jats:p>In interval analysis, integral inequalities are determined based on different types of order relations, including pseudo, fuzzy, inclusion, and various other partial order relations. By developing a link between center-radius (CR) order relations, it seeks to develop a theory of inequalities with novel estimates. A (CR)-order relation relationship differs from traditional interval-order relationships in that it is calculated as follows: <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>q</mi> <mo>=</mo> <mfenced open="〈" close="〉" separators="|"> <mrow> <msub> <mrow> <mi>q</mi> </mrow> <mrow> <mi>c</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>q</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> </mrow> </mfenced> <mo>=</mo> <mfenced open="〈" close="〉" separators="|"> <mrow> <mrow> <mrow> <mover accent="true"> <mi>q</mi> <mo>¯</mo> </mover> <mo>+</mo> <munder accentunder="true"> <mi>q</mi> <mo>¯</mo> </munder> </mrow> <mo>/</mo> <mn>2</mn> </mrow> <mo>,</mo> <mrow> <mrow> <mover accent="true"> <mi>q</mi> <mo>¯</mo> </mover> <mo>−</mo> <munder accentunder="true"> <mi>q</mi> <mo>¯</mo> </munder> </mrow> <mo>/</mo>
{"title":"Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation","authors":"W. Afzal, K. Shabbir, M. Arshad, Joshua Kiddy K. Asamoah, A. Galal","doi":"10.1155/2023/8865992","DOIUrl":"https://doi.org/10.1155/2023/8865992","url":null,"abstract":"<jats:p>In interval analysis, integral inequalities are determined based on different types of order relations, including pseudo, fuzzy, inclusion, and various other partial order relations. By developing a link between center-radius (CR) order relations, it seeks to develop a theory of inequalities with novel estimates. A (CR)-order relation relationship differs from traditional interval-order relationships in that it is calculated as follows: <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>q</mi>\u0000 <mo>=</mo>\u0000 <mfenced open=\"〈\" close=\"〉\" separators=\"|\">\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <mfenced open=\"〈\" close=\"〉\" separators=\"|\">\u0000 <mrow>\u0000 <mrow>\u0000 <mrow>\u0000 <mover accent=\"true\">\u0000 <mi>q</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <mo>+</mo>\u0000 <munder accentunder=\"true\">\u0000 <mi>q</mi>\u0000 <mo>¯</mo>\u0000 </munder>\u0000 </mrow>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <mo>,</mo>\u0000 <mrow>\u0000 <mrow>\u0000 <mover accent=\"true\">\u0000 <mi>q</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <mo>−</mo>\u0000 <munder accentunder=\"true\">\u0000 <mi>q</mi>\u0000 <mo>¯</mo>\u0000 </munder>\u0000 </mrow>\u0000 <mo>/</mo>\u0000 ","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85515449","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}
R. Ramaswamy, E. S. El-Shazly, M. S. Abdel Latif, A. Elsonbaty, A. H. Abdel Kader
In this article, we use Lie point symmetry analysis to extract some new optical soliton solutions for the generalized Kudryashov’s equation (GKE) with an arbitrary power nonlinearity. Using a traveling wave transformation, the GKE is transformed into a nonlinear second order ordinary differential equation (ODE). Using Lie point symmetry analysis, the nonlinear second-order ODE is reduced to a first-order ODE. This first-order ODE is solved in two cases to retrieve some new bright, dark, and kink soliton solutions of the GKE. These soliton solutions for the GKE are obtained here for the first time.
{"title":"Exact Optical Solitons for Generalized Kudryashov’s Equation by Lie Symmetry Method","authors":"R. Ramaswamy, E. S. El-Shazly, M. S. Abdel Latif, A. Elsonbaty, A. H. Abdel Kader","doi":"10.1155/2023/2685547","DOIUrl":"https://doi.org/10.1155/2023/2685547","url":null,"abstract":"In this article, we use Lie point symmetry analysis to extract some new optical soliton solutions for the generalized Kudryashov’s equation (GKE) with an arbitrary power nonlinearity. Using a traveling wave transformation, the GKE is transformed into a nonlinear second order ordinary differential equation (ODE). Using Lie point symmetry analysis, the nonlinear second-order ODE is reduced to a first-order ODE. This first-order ODE is solved in two cases to retrieve some new bright, dark, and kink soliton solutions of the GKE. These soliton solutions for the GKE are obtained here for the first time.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88641226","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 the field of biological control, there are a large number of systems that gradually evolve over a certain period of time. However, due to some natural or human intervention behavior, the system state will be subjected to some relatively short time interference, so that the system state changes in an instant. This sudden change of state makes the system not simply described by continuous or discrete dynamical systems, but by means of impulse dynamical systems. In this paper, the multi-point boundary value problem of a class of second-order nonlinear impulsive integral differential equations is studied on the basis of impulsive differential equation theory. The main results of this kind of equation are obtained by using the fixed point theorem of strict set contraction operator. Under certain assumptions, the existence of the solution of the equation is proved by constructing the operator on the special cone. Finally, combined with the practical application, the theory was applied to the stability prediction of biological ecosystem, and the correctness of the conclusion was verified.
{"title":"Study on the Multi-Point Boundary Value Problem for Second-Order Nonlinear Impulsive Integro-Differential Equation","authors":"Haiyan Li, Yuheng Guo","doi":"10.1155/2023/3120723","DOIUrl":"https://doi.org/10.1155/2023/3120723","url":null,"abstract":"In the field of biological control, there are a large number of systems that gradually evolve over a certain period of time. However, due to some natural or human intervention behavior, the system state will be subjected to some relatively short time interference, so that the system state changes in an instant. This sudden change of state makes the system not simply described by continuous or discrete dynamical systems, but by means of impulse dynamical systems. In this paper, the multi-point boundary value problem of a class of second-order nonlinear impulsive integral differential equations is studied on the basis of impulsive differential equation theory. The main results of this kind of equation are obtained by using the fixed point theorem of strict set contraction operator. Under certain assumptions, the existence of the solution of the equation is proved by constructing the operator on the special cone. Finally, combined with the practical application, the theory was applied to the stability prediction of biological ecosystem, and the correctness of the conclusion was verified.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84234085","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}
Saleh Alshammari, Mohammad Alshammari, Mohammed S Abdo
In this study, we develop a theory for the nonlocal hybrid boundary value problem for the fractional integro-differential equations featuring Atangana–Baleanu derivatives. The corresponding hybrid fractional integral equation is presented. Then, we establish the existence results using Dhage’s hybrid fixed point theorem for a sum of three operators. We also offer additional exceptional cases and similar outcomes. In order to demonstrate and verify the results, we provide an example as an application.
{"title":"Nonlocal Hybrid Integro-Differential Equations Involving Atangana–Baleanu Fractional Operators","authors":"Saleh Alshammari, Mohammad Alshammari, Mohammed S Abdo","doi":"10.1155/2023/5891342","DOIUrl":"https://doi.org/10.1155/2023/5891342","url":null,"abstract":"In this study, we develop a theory for the nonlocal hybrid boundary value problem for the fractional integro-differential equations featuring Atangana–Baleanu derivatives. The corresponding hybrid fractional integral equation is presented. Then, we establish the existence results using Dhage’s hybrid fixed point theorem for a sum of three operators. We also offer additional exceptional cases and similar outcomes. In order to demonstrate and verify the results, we provide an example as an application.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"47 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84210913","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}
The use of interval-valued hesitant fuzzy sets (IVHFS) can aid decision-makers in evaluating a variable using multiple interval numbers, making it a valuable tool for addressing decision-making problems. However, it fails to obtain information with greyness. The grey fuzzy set (GFS) can improve this problem but studies on it have lost the advantages of IVHFS. In order to improve the accuracy of decision-making and obtain more reasonable results, it is important to enhance the description of real-life information. We combined IVHFS and GFS and defined a novel fuzzy set named interval grey hesitant fuzzy set (IGHFS), in which possible degrees of grey numbers are designed to indicate the upper and lower limits of the interval number. Meanwhile, its basic operational laws, score function, entropy method, and distance measures are proposed. And then, a multicriteria decision-making (MCDM) model IGHFS-TOPSIS is developed based on them. Finally, an example of MOOC platform selection issues for teaching courses illustrates the effectiveness and feasibility of the decision model under the IGHFS.
{"title":"Interval Grey Hesitant Fuzzy Set and Its Applications in Decision-Making","authors":"Jing-jing Zhao, Wanli Xie","doi":"10.1155/2023/7694396","DOIUrl":"https://doi.org/10.1155/2023/7694396","url":null,"abstract":"The use of interval-valued hesitant fuzzy sets (IVHFS) can aid decision-makers in evaluating a variable using multiple interval numbers, making it a valuable tool for addressing decision-making problems. However, it fails to obtain information with greyness. The grey fuzzy set (GFS) can improve this problem but studies on it have lost the advantages of IVHFS. In order to improve the accuracy of decision-making and obtain more reasonable results, it is important to enhance the description of real-life information. We combined IVHFS and GFS and defined a novel fuzzy set named interval grey hesitant fuzzy set (IGHFS), in which possible degrees of grey numbers are designed to indicate the upper and lower limits of the interval number. Meanwhile, its basic operational laws, score function, entropy method, and distance measures are proposed. And then, a multicriteria decision-making (MCDM) model IGHFS-TOPSIS is developed based on them. Finally, an example of MOOC platform selection issues for teaching courses illustrates the effectiveness and feasibility of the decision model under the IGHFS.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"3 1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78634220","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 considered the one-dimensional swelling problem in porous elastic soils with microtemperatures effects in the case of fluid saturation. First, we showed that the system is well-posed in the sens of semigroup. Then, we constructed a suitable Lyapunov functional based on the energy method and we proved that the dissipation given only by the microtemperatures is strong enough to provoke an exponential stability for the solution irrespective of the wave speeds of the system.
{"title":"Exponential Decay of Swelling Porous Elastic Soils with Microtemperatures Effects","authors":"A. Rezaiguia, S. Zitouni, Hasan Nihal Zaidi","doi":"10.1155/2023/6013085","DOIUrl":"https://doi.org/10.1155/2023/6013085","url":null,"abstract":"In this article, we considered the one-dimensional swelling problem in porous elastic soils with microtemperatures effects in the case of fluid saturation. First, we showed that the system is well-posed in the sens of semigroup. Then, we constructed a suitable Lyapunov functional based on the energy method and we proved that the dissipation given only by the microtemperatures is strong enough to provoke an exponential stability for the solution irrespective of the wave speeds of the system.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"48 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82236883","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}
Prasantha Bharathi Dhandapani, Jayakumar Thippan, B. Unyong, R. Vadivel, P. Hammachukiattikul
The goal of this paper is to find the best of two sixth-order methods, namely, RK-Huta and RK–Butcher methods for solving the fuzzy hybrid systems. We state a necessary definition and theorem in terms of consistency for convergence, and finally, we compare the obtained numerical results of two different methods with analytical solution using two different numerical examples. In addition to that, we generalize the solutions obtained by RK-6 Huta and RK-6 Butcher methods (same order different stage methods) for both the problems we handled. We are proposing these two methods in order to reduce the error in accuracy and to establish these two methods are better than any other existing numerical methods. The best of two sixth-order methods are found by the error analysis study for both the problems. Also, we show whether the change in number of stages of same order methods affects the accuracy of the approximation or not.
{"title":"On New Solutions of Fuzzy Hybrid Differential Equations by Novel Approaches","authors":"Prasantha Bharathi Dhandapani, Jayakumar Thippan, B. Unyong, R. Vadivel, P. Hammachukiattikul","doi":"10.1155/2023/7865973","DOIUrl":"https://doi.org/10.1155/2023/7865973","url":null,"abstract":"The goal of this paper is to find the best of two sixth-order methods, namely, RK-Huta and RK–Butcher methods for solving the fuzzy hybrid systems. We state a necessary definition and theorem in terms of consistency for convergence, and finally, we compare the obtained numerical results of two different methods with analytical solution using two different numerical examples. In addition to that, we generalize the solutions obtained by RK-6 Huta and RK-6 Butcher methods (same order different stage methods) for both the problems we handled. We are proposing these two methods in order to reduce the error in accuracy and to establish these two methods are better than any other existing numerical methods. The best of two sixth-order methods are found by the error analysis study for both the problems. Also, we show whether the change in number of stages of same order methods affects the accuracy of the approximation or not.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"115 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75636775","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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