This paper presents approximate controllability results for impulsive stochastic integro-differential systems with state-dependent delay in a Hilbert space. The use of the resolvent operator in the sense of Grimmer, as well as stochastic analysis techniques, yields a new set of results. Finally, an example is given to show how the theory that has been worked out can be put into practice.
{"title":"Some results on the approximate controllability of impulsive stochastic integro-differential equations with nonlocal conditions and state-dependent delay","authors":"M. Fall, A. Mané, B. Dehigbe, M. Diop","doi":"10.22436/jnsa.015.04.04","DOIUrl":"https://doi.org/10.22436/jnsa.015.04.04","url":null,"abstract":"This paper presents approximate controllability results for impulsive stochastic integro-differential systems with state-dependent delay in a Hilbert space. The use of the resolvent operator in the sense of Grimmer, as well as stochastic analysis techniques, yields a new set of results. Finally, an example is given to show how the theory that has been worked out can be put into practice.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"111 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88875921","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 nonlinear transmission line (NLTL) model is very essential tools in understanding of propagation of electrical solitons which can propagate in the form of voltage waves in nonlinear dispersive media. These models are often formulated using nonlinear partial differential equations. One of the basic tools available to study these equations are numerical methods such as finite difference method, finite element method, etc, have been developed for nonlinear partial differential equations. These methods require a great amount of time and memory due to the discretization and usually the effect of round-off error causes loss of accuracy in the results. So in this paper, we use one of the most famous analytical methods the Lie group analysis due to Sophus Lie. One of the advantages of this approach is that requires only algebraic calculations. The main aim of this study is to explore the nonlinear transmission line model with arbitrary capacitor’s voltage dependence, through the use of Lie group classification, we show that the specifying form of arbitrary capacitor’s voltage are power law nonlinearity, exponential law nonlinearity and constant capacitance. The exact solutions and similarity reductions generated from the symmetries are also provided. Furthermore, translational symmetries were utilized to find a family of traveling wave solutions via the tanh-method of the governing nonlinear problem.
{"title":"Lie group classification of the nonlinear transmission line model and exact traveling wave solutions","authors":"T. Amtout, M. Er-Riani, M. Jarroudi","doi":"10.22436/jnsa.015.04.02","DOIUrl":"https://doi.org/10.22436/jnsa.015.04.02","url":null,"abstract":"A nonlinear transmission line (NLTL) model is very essential tools in understanding of propagation of electrical solitons which can propagate in the form of voltage waves in nonlinear dispersive media. These models are often formulated using nonlinear partial differential equations. One of the basic tools available to study these equations are numerical methods such as finite difference method, finite element method, etc, have been developed for nonlinear partial differential equations. These methods require a great amount of time and memory due to the discretization and usually the effect of round-off error causes loss of accuracy in the results. So in this paper, we use one of the most famous analytical methods the Lie group analysis due to Sophus Lie. One of the advantages of this approach is that requires only algebraic calculations. The main aim of this study is to explore the nonlinear transmission line model with arbitrary capacitor’s voltage dependence, through the use of Lie group classification, we show that the specifying form of arbitrary capacitor’s voltage are power law nonlinearity, exponential law nonlinearity and constant capacitance. The exact solutions and similarity reductions generated from the symmetries are also provided. Furthermore, translational symmetries were utilized to find a family of traveling wave solutions via the tanh-method of the governing nonlinear problem.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82943882","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}
We introduce and study deferred N"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin type theorems for the sequence of random variables via deferred N"{o}rlund statistically convergence and present compelling examples to demonstrate the effectiveness of the results.
{"title":"Deferred Nörlund statistical convergence in probability, mean and distribution for sequences of random variables","authors":"K. Raj, Swati Jasrotia, R. Saadati","doi":"10.22436/jnsa.016.01.04","DOIUrl":"https://doi.org/10.22436/jnsa.016.01.04","url":null,"abstract":"We introduce and study deferred N\"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin type theorems for the sequence of random variables via deferred N\"{o}rlund statistically convergence and present compelling examples to demonstrate the effectiveness of the results.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"91 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78800321","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 introduce a definition of geometric-arithmetically ( s , m ) convex function and give some new inequalities of Hermite-Hadamard type for the geometric-arithmetically ( s , m ) convex function. Finally, we discuss applications of these inequalities to special means.
{"title":"Hermite-Hadamard type integral inequalities for geometric-arithmetically (s,m) convex functions","authors":"X. Cheng, Hanshuo Zuo, Z. Hua","doi":"10.22436/jnsa.015.04.01","DOIUrl":"https://doi.org/10.22436/jnsa.015.04.01","url":null,"abstract":"In this paper, we introduce a definition of geometric-arithmetically ( s , m ) convex function and give some new inequalities of Hermite-Hadamard type for the geometric-arithmetically ( s , m ) convex function. Finally, we discuss applications of these inequalities to special means.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73139392","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 study the qualitative dynamical analysis, routes to chaos and the coexistence of attractors in a four-well φ 8 -generalized Li´enard oscillator under external and parametric excitations. The local analysis of the autonomous system reveals saddles, nodes, spirals or centers for appropriate choice of stiffness and damping coefficients. The existence of a Hopf bifurcation is proved during the stability analysis of the equilibrium points. The routes to chaos and the prediction of coexisting attractors have been investigated numerically by using the fourth order Runge-Kutta algorithm. The bifurcation structures obtained show that the system displays a rich variety of bifurcation phenomena, such as symmetry breaking, symmetry restoring, period-doubling, period windows, period-m bubbles, reverse period windows, antimonotonicity, intermittency, quasiperiodic, and chaos. In addition, remerging chaotic band attractors and remarkable routes to chaos occur in the system. Further, it is found that the system presents various coexistence of two attractors as well as the monostability and bistability phenomena. On the other hand, for large amplitude of the parametric excitation and with ω = 1, the coexistence of asymmetric periodic bursting oscillations of different topologies takes place in the system. It has also been shown numerically that for appropriate values of system parameters and initial conditions, the presented system can exhibit up to five types of coexisting multiple attractors.
{"title":"Qualitative analysis, chaos and coexisting attractors in an asymmetric four-well ϕ 8 -generalized Liénard oscillator driven by parametric and external excitations","authors":"Y. Kpomahou, J. Adéchinan, J. Edou, L. A. Hinvi","doi":"10.22436/jnsa.015.03.06","DOIUrl":"https://doi.org/10.22436/jnsa.015.03.06","url":null,"abstract":"In this paper, we study the qualitative dynamical analysis, routes to chaos and the coexistence of attractors in a four-well φ 8 -generalized Li´enard oscillator under external and parametric excitations. The local analysis of the autonomous system reveals saddles, nodes, spirals or centers for appropriate choice of stiffness and damping coefficients. The existence of a Hopf bifurcation is proved during the stability analysis of the equilibrium points. The routes to chaos and the prediction of coexisting attractors have been investigated numerically by using the fourth order Runge-Kutta algorithm. The bifurcation structures obtained show that the system displays a rich variety of bifurcation phenomena, such as symmetry breaking, symmetry restoring, period-doubling, period windows, period-m bubbles, reverse period windows, antimonotonicity, intermittency, quasiperiodic, and chaos. In addition, remerging chaotic band attractors and remarkable routes to chaos occur in the system. Further, it is found that the system presents various coexistence of two attractors as well as the monostability and bistability phenomena. On the other hand, for large amplitude of the parametric excitation and with ω = 1, the coexistence of asymmetric periodic bursting oscillations of different topologies takes place in the system. It has also been shown numerically that for appropriate values of system parameters and initial conditions, the presented system can exhibit up to five types of coexisting multiple attractors.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88614234","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}
We show that it is possible to define extensions of the Laplace transform that use a general Dirichlet series as a kernel. These transforms, denoted by DLTs, further generalize those, considered in previous papers, in which the kernels were related to Laguerre-type exponentials or Bell polynomials. Computational techniques, exploiting expansions in Laguerre polynomials, and using Tricomi’s method, have been considered. Since it turns out that the transforms considered are obtained as linear combinations of ordinary Laplace transforms, it is also possible to define an approximation of the relevant inverse transforms. Numerical experiments, performed with the algebra program Mathematica, show that the introduced technique is fast and efficient.
{"title":"The Dirichlet-type Laplace transforms","authors":"D. Caratelli, S. Pinelas, P. Ricci","doi":"10.22436/jnsa.015.03.05","DOIUrl":"https://doi.org/10.22436/jnsa.015.03.05","url":null,"abstract":"We show that it is possible to define extensions of the Laplace transform that use a general Dirichlet series as a kernel. These transforms, denoted by DLTs, further generalize those, considered in previous papers, in which the kernels were related to Laguerre-type exponentials or Bell polynomials. Computational techniques, exploiting expansions in Laguerre polynomials, and using Tricomi’s method, have been considered. Since it turns out that the transforms considered are obtained as linear combinations of ordinary Laplace transforms, it is also possible to define an approximation of the relevant inverse transforms. Numerical experiments, performed with the algebra program Mathematica, show that the introduced technique is fast and efficient.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85623650","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 aim of this work is to study a pseudomonotone variational inequality and a fixed point problem involving pseudocontractive mappings in real Hilbert spaces. We introduce an inertia-based iterative algorithm for finding a common solution to this problem. The strong convergence of the proposed algorithm is proved. Finally, numerical examples are provided and also meaningful comparisons of these results with those in [Y. Yao, M. Postolache, J. C. Yao, Mathematics, 7 (2019), 14 pages], proving that at our proposed numerical schemes are more efficient.
本文研究了实数Hilbert空间中的一个伪单调变分不等式和一个涉及伪压缩映射的不动点问题。我们引入了一种基于惯性的迭代算法来寻找这一问题的公共解。证明了该算法的强收敛性。最后给出了数值算例，并与文献[Y]的结果进行了有意义的比较。姚，M. Postolache, J. C. Yao，数学，7(2019)，14页]，证明我们提出的数值格式更有效。
{"title":"An inertia-based algorithm for pseudomonotone variational inequality and fixed point problems in real Hilbert space","authors":"J. Ezeora, R. C. Ogbonna, F. E. Bazuaye","doi":"10.22436/jnsa.015.03.04","DOIUrl":"https://doi.org/10.22436/jnsa.015.03.04","url":null,"abstract":"The aim of this work is to study a pseudomonotone variational inequality and a fixed point problem involving pseudocontractive mappings in real Hilbert spaces. We introduce an inertia-based iterative algorithm for finding a common solution to this problem. The strong convergence of the proposed algorithm is proved. Finally, numerical examples are provided and also meaningful comparisons of these results with those in [Y. Yao, M. Postolache, J. C. Yao, Mathematics, 7 (2019), 14 pages], proving that at our proposed numerical schemes are more efficient.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82086533","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 last few decades many authors pointed out that derivatives and integrals of non-integer order are very suitable for the description of properties of various real problems. It has been shown that fractional-order models are more adequate than previously used integer-order models. In this work, we aim to investigate of different features of the plant virus model with its fractional order equivalent. We present an application for reproduction number for these kind of epidemic models with next generation matrix method. Also, existence and uniqueness of solutions have been showed for this fractional order system. Finally we present some figures according to the given numerical scheme.
{"title":"A different approach for behavior of fractional plant virus model","authors":"I. Koka, H. Bulut, E. Akçetin","doi":"10.22436/jnsa.015.03.02","DOIUrl":"https://doi.org/10.22436/jnsa.015.03.02","url":null,"abstract":"In the last few decades many authors pointed out that derivatives and integrals of non-integer order are very suitable for the description of properties of various real problems. It has been shown that fractional-order models are more adequate than previously used integer-order models. In this work, we aim to investigate of different features of the plant virus model with its fractional order equivalent. We present an application for reproduction number for these kind of epidemic models with next generation matrix method. Also, existence and uniqueness of solutions have been showed for this fractional order system. Finally we present some figures according to the given numerical scheme.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"10 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84079226","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 begin by presenting a general Leray-Schauder alternative and a topological transversality theorem for Kakutani (upper semicontinuous maps with nonempty convex compact values) compact weakly inward maps. Then with some observations and extra assumptions we present a Leray-Schauder alternative and a topological transversality theorem for acyclic (upper semicontinuous maps with nonempty acyclic compact values) compact strongly inward maps.
{"title":"Continuation theorems for weakly inward Kakutani and Strongly inward acyclic maps","authors":"D. O’Regan","doi":"10.22436/jnsa.015.03.03","DOIUrl":"https://doi.org/10.22436/jnsa.015.03.03","url":null,"abstract":"In this paper we begin by presenting a general Leray-Schauder alternative and a topological transversality theorem for Kakutani (upper semicontinuous maps with nonempty convex compact values) compact weakly inward maps. Then with some observations and extra assumptions we present a Leray-Schauder alternative and a topological transversality theorem for acyclic (upper semicontinuous maps with nonempty acyclic compact values) compact strongly inward maps.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"110 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74469591","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 develop controllability findings for impulsive neutral stochastic delay partial integrodifferential equations in Hilbert spaces driven by Rosenblatt process and Lévy noise. A novel set of adequate requirements is obtained by utilizing a fixed point method without imposing a stringent compactness constraint on the semigroup. The observed results represent a generalization and continuation of previous findings on this topic. Finally, an example is given to demonstrate how the acquired findings may be used.
{"title":"Controllability of impulsive stochastic functional integrodifferential equations driven by Rosenblatt process and Lévy noise","authors":"M. H. M. Hamit, K. H. Bete, B. Mahamat, M. Diop","doi":"10.22436/jnsa.015.02.06","DOIUrl":"https://doi.org/10.22436/jnsa.015.02.06","url":null,"abstract":"In this paper, we develop controllability findings for impulsive neutral stochastic delay partial integrodifferential equations in Hilbert spaces driven by Rosenblatt process and Lévy noise. A novel set of adequate requirements is obtained by utilizing a fixed point method without imposing a stringent compactness constraint on the semigroup. The observed results represent a generalization and continuation of previous findings on this topic. Finally, an example is given to demonstrate how the acquired findings may be used.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86538415","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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