Ishfaq S. Ahmad, M. Y. Bhat, P. B. Ahmad, J. Dar, S. Pinelas
A novel probability model with bounded support is introduced. The formulation of this new probability model is based on inverting the Slashed Pareto distribution. This new distribution has the merit of being very simple and not involving any complex mathematical function in its construction. Some interesting properties like moments, skewness and kurtosis, unimodality, L-Moments, L-skewness and L-kurtosis would be explored in detail. Various Survival properties including survival function, hazard rate function and mean residual life(MRL) like have been given. For estimating the parameters contained in the new model, methods like Method of Moments (MOM) and Maximum Likelihood Estimation (MLE) have been used.
{"title":"Bounded Inverse-Slashed Pareto Model: Structural Properties and Real-Life Applications","authors":"Ishfaq S. Ahmad, M. Y. Bhat, P. B. Ahmad, J. Dar, S. Pinelas","doi":"10.31197/atnaa.1325508","DOIUrl":"https://doi.org/10.31197/atnaa.1325508","url":null,"abstract":"A novel probability model with bounded support is introduced. The formulation of this new probability model is based on inverting the Slashed Pareto distribution. This new distribution has the merit of being very simple and not involving any complex mathematical function in its construction. Some interesting properties like moments, skewness and kurtosis, unimodality, L-Moments, L-skewness and L-kurtosis would be explored in detail. Various Survival properties including survival function, hazard rate function and mean residual life(MRL) like have been given. For estimating the parameters contained in the new model, methods like Method of Moments (MOM) and Maximum Likelihood Estimation (MLE) have been used.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"139 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86390927","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 manuscript, we define a new class of control functions classified as ascendant functions. Consequently, we furnish a fuzzy coupled fixed point result, that is different from one available in the literature, using the notion of simulation function; in follow, we validate the result through a non-trivial example. As an inference, we use the result to analyze the existence of a solution for a non-linear system of fuzzy initial value problem involving generalized Hukuhara derivative.
{"title":"SOLUTION TO A SYSTEM OF NON-LINEAR FUZZY DIFFERENTIAL EQUATION WITH GENERALIZED HUKUHARA DERIVATIVE VIA FIXED POINT THEOREM","authors":"Sushma Basi̇l, S. Antony","doi":"10.31197/atnaa.1232379","DOIUrl":"https://doi.org/10.31197/atnaa.1232379","url":null,"abstract":"In this manuscript, we define a new class of control \u0000functions classified as ascendant functions. Consequently, we furnish \u0000a fuzzy coupled fixed point result, that is different from one available \u0000in the literature, using the notion of simulation function; in follow, we \u0000validate the result through a non-trivial example. As an inference, we \u0000use the result to analyze the existence of a solution for a non-linear \u0000system of fuzzy initial value problem involving generalized Hukuhara \u0000derivative.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"393 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73428368","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 system of ordinary differential equations that arises in the theory of genetic networks is studied. Attracting sets of a special kind is the focus of the study. These attractors appear as combinations of attractors of lower dimensions, which are stable limit cycles. The properties of attractors are studied. Visualizations and examples are provided.
{"title":"On attractors in dynamical systems modeling genetic networks","authors":"F. Sadyrbaev","doi":"10.31197/atnaa.1248853","DOIUrl":"https://doi.org/10.31197/atnaa.1248853","url":null,"abstract":"The system of ordinary differential equations that arises in the theory of genetic networks is studied. Attracting sets of a special kind is the focus of the study. These attractors appear as combinations of attractors of lower dimensions, \u0000which are stable limit cycles. The properties of attractors are studied. Visualizations and examples are provided.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90995826","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 well-known Caristi fixed point theorem has numerous generalizations and modifications. Recently there have appeared its equivalent dual forms and generalizations based on new concept of lower semicontinuity from above by several authors. In the present article, we give new proofs of such new versions and their equivalent formulations by applying our Metatheorem in the ordered fixed point theory.
{"title":"Variants of the New Caristi Theorem","authors":"Sehie Park","doi":"10.31197/atnaa.1290064","DOIUrl":"https://doi.org/10.31197/atnaa.1290064","url":null,"abstract":"The well-known Caristi fixed point theorem has numerous generalizations and modifications. Recently there \u0000have appeared its equivalent dual forms and generalizations based on new concept of lower semicontinuity \u0000from above by several authors. In the present article, we give new proofs of such new versions and their \u0000equivalent formulations by applying our Metatheorem in the ordered fixed point theory.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80696235","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}
Sadia Akter Lima, Md. Shafiqul Islam, Hazrat Ali̇, M. Kamrujjaman
In this study, we consider the system of second order nonlinear boundary value problems (BVPs). We focus on the numerical solutions of different types of nonlinear BVPs by Galerkin finite element method (GFEM). First of all, we originate the generalized formulation of GFEM for those type of problems. Then we determine the approximate solutions of a couple of second order nonlinear BVPs by GFEM. The approximate results are unfolded in tabuler form and portrayed graphically along with the exact solutions. Those results demonstrate the applicability, compatibility and accuracy of this scheme.
{"title":"Numerical method to solve generalized nonlinear system of second order boundary value problems: Galerkin approach","authors":"Sadia Akter Lima, Md. Shafiqul Islam, Hazrat Ali̇, M. Kamrujjaman","doi":"10.31197/atnaa.1141150","DOIUrl":"https://doi.org/10.31197/atnaa.1141150","url":null,"abstract":"In this study, we consider the system of second order nonlinear boundary value problems (BVPs). We focus on the numerical solutions of \u0000different types of nonlinear BVPs by Galerkin finite element method (GFEM). First of all, we originate the generalized formulation of GFEM for those type of problems. Then we determine the approximate solutions of a couple of second order nonlinear BVPs by GFEM. The approximate results are unfolded in tabuler form and portrayed graphically along with the exact solutions. Those results demonstrate the applicability, compatibility and accuracy of this scheme.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79797053","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 paper, the Lomov's regularization method is generalized to a singularly perturbed integro-differential equation with a fractional derivative and with a rapidly oscillating inhomogeneity. The main goal of the work is to reveal the influence of a rapidly changing kernel on the structure of the asymptotics of the problem solution and to study additional boundary functions that are generated by rapidly oscillating inhomogeneities.
{"title":"Influence of rapidly oscillating inhomogeneities in the formation of additional boundary layers for singularly perturbed integro-differential systems","authors":"M. Akylbayev, Burhan Kali̇mbetov, N. Pardaeva","doi":"10.31197/atnaa.1264072","DOIUrl":"https://doi.org/10.31197/atnaa.1264072","url":null,"abstract":"In this paper, the Lomov's regularization method is generalized to a singularly perturbed integro-differential equation with a fractional derivative and with a rapidly oscillating inhomogeneity. The main goal of the work is to reveal the influence of a rapidly changing kernel on the structure of the asymptotics of the problem solution and to study additional boundary functions that are generated by rapidly oscillating inhomogeneities.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"158 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77806511","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 research, we propose and study an online social network mathematical model with delay based on two innovative assumptions: (1) newcomers are entering community as either potential online network users or that who are never interested in online network at constant rates, respectively; and (2) it takes a certain time for the active online network users to start abandoning the network. The basic reproduction $R_0,$ the user-free equilibrium(UFE) $P_0,$ and the user-prevailing equilibrium(UPE) $P^*$ are identified. The analysis of local and global stability for those equilibria is carried out. For the UPE $P^*,$ using the delay $tau$ as the Hopf bifurcation parameter, the occurrence of Hopf bifurcation is investigated. The conditions are established that guarantee the Hopf bifurcation occurs as $tau$ crosses the critical values. Numerical simulations are provided to illustrate the theoretical results.
{"title":"Stability and Bifurcation Analysis For An OSN Model with Delay","authors":"Liancheng Wang, Min Wang","doi":"10.31197/atnaa.1152602","DOIUrl":"https://doi.org/10.31197/atnaa.1152602","url":null,"abstract":"In this research, we propose and study an online social network mathematical model with delay based on two innovative assumptions: (1) newcomers are entering community as either potential online network users or that who are never interested in online network at constant rates, respectively; and (2) it takes a certain time for the active online network users to start abandoning the network. The basic reproduction $R_0,$ the user-free equilibrium(UFE) $P_0,$ and the user-prevailing equilibrium(UPE) $P^*$ are identified. The analysis of local and global stability for those equilibria is carried out. For the UPE $P^*,$ using the delay $tau$ as the Hopf bifurcation parameter, the occurrence of Hopf bifurcation is investigated. The conditions are established that guarantee the Hopf bifurcation occurs as $tau$ crosses the critical values. Numerical simulations are provided to illustrate the theoretical results.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75224233","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}
Convergence theorems required more assumptions on parameters than fixed point theorems. In this paper we generalize the concept of acute point and we introduce some convergence theorems that holds under the same assumptions on parameters as fixed point theorems.
{"title":"Mean convergence theorems to generalized acute points for generalized pseudocontractions","authors":"T. Kawasaki","doi":"10.31197/atnaa.1299905","DOIUrl":"https://doi.org/10.31197/atnaa.1299905","url":null,"abstract":"Convergence theorems required more assumptions on parameters than fixed point theorems. In this paper we generalize the concept of acute point and we introduce some convergence theorems that holds under the same assumptions on parameters as fixed point theorems.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90787269","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 paper, we are interested to study a nonlinear Volterra equation with conformable derivative. This kind of such equation has various applications, for example physics, mechanical engineering, heat conduction theory. First, we show that our problem have a mild soltution which exists locally in time. Then we prove that the convergence of the mild solution when the parameter tends to zero.
{"title":"On the nonlinear Volterra equation with conformable derivative","authors":"Tuan NGUYEN HOANG, Hai NGUYEN MİNH, N. Phuong","doi":"10.31197/atnaa.1281575","DOIUrl":"https://doi.org/10.31197/atnaa.1281575","url":null,"abstract":"In this paper, we are interested to study a nonlinear Volterra equation with conformable derivative. This kind of such equation has various applications, for example physics, mechanical engineering, heat conduction theory. \u0000First, we show that our problem have a mild soltution which exists locally in time. Then we prove that the convergence of the mild solution when the parameter tends to zero.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90739318","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}
An arbitrary point is removed from a three-dimensional Euclidean space on a two-dimensional sphere. The new well-posed solvable boundary value problems for the corresponding Laplace-Beltrami operator on the resulting punctured sphere are presented. To formulate the well-posed problems some properties of Green's function of the Laplace-Beltrami operator on a two-dimensional sphere are previously studied in detail.
{"title":"Well-posed problems for the Laplace-Beltrami operator on a punctured two-dimensional sphere","authors":"B. Kanguzhin, K. Dosmagulova","doi":"10.31197/atnaa.1253855","DOIUrl":"https://doi.org/10.31197/atnaa.1253855","url":null,"abstract":"An arbitrary point is removed from a three-dimensional Euclidean space on a two-dimensional sphere. The new well-posed solvable boundary value problems for the corresponding Laplace-Beltrami operator on the resulting punctured sphere are presented. To formulate the well-posed problems some properties of Green's function of the Laplace-Beltrami operator on a two-dimensional sphere are previously studied in detail.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"211 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75671886","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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