Pub Date : 2022-04-11DOI: 10.15388/namc.2022.27.26678
Suripeddi Suripeddi Srinivas, Challa Kalyan Kumar, A. S. Reddy
This article aims to inspect the pulsating hydromagnetic slip flow of Casson fluid in a vertical porous channel with heat and mass transfer. The fluid is injected into the channel from the left wall and removed at the opposite wall with the same velocity. The impact of non-Darcy, Soret, and Dufour effects are taken under consideration. The governing partial differential equations (PDEs) are converted to ordinary differential equations (ODEs) using perturbation method and solved by utilizing 4th-order Runge–Kutta (R–K) technique together with shooting method. The impact of dissimilar parameters on flow, heat and mass transfer characteristics are displayed and discussed.
{"title":"Dufour and Soret effects on pulsatile hydromagnetic flow of Casson fluid in a vertical non-Darcian porous space","authors":"Suripeddi Suripeddi Srinivas, Challa Kalyan Kumar, A. S. Reddy","doi":"10.15388/namc.2022.27.26678","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26678","url":null,"abstract":"This article aims to inspect the pulsating hydromagnetic slip flow of Casson fluid in a vertical porous channel with heat and mass transfer. The fluid is injected into the channel from the left wall and removed at the opposite wall with the same velocity. The impact of non-Darcy, Soret, and Dufour effects are taken under consideration. The governing partial differential equations (PDEs) are converted to ordinary differential equations (ODEs) using perturbation method and solved by utilizing 4th-order Runge–Kutta (R–K) technique together with shooting method. The impact of dissimilar parameters on flow, heat and mass transfer characteristics are displayed and discussed.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48945042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-11DOI: 10.15388/namc.2022.27.29528
A. Dargys, A. Acus
The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra. Closed form expressions for a multivector exponential and logarithm are presented in real geometric algebras Clp;q when n = p + q = 1 (complex and hyperbolic numbers) and n = 2 (Hamilton, split, and conectorine quaternions). Starting from Cl0;1 and Cl1;0 algebras wherein square of a basis vector is either –1 or +1, we have generalized exponential and logarithm formulas to 2D quaternionic algebras Cl0;2, Cl1;1, and Cl2;0. The sectors in the multivector coefficient space, where 2D logarithm exists are found. They are related with a square root of the multivector.
{"title":"Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras","authors":"A. Dargys, A. Acus","doi":"10.15388/namc.2022.27.29528","DOIUrl":"https://doi.org/10.15388/namc.2022.27.29528","url":null,"abstract":"The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra. Closed form expressions for a multivector exponential and logarithm are presented in real geometric algebras Clp;q when n = p + q = 1 (complex and hyperbolic numbers) and n = 2 (Hamilton, split, and conectorine quaternions). Starting from Cl0;1 and Cl1;0 algebras wherein square of a basis vector is either –1 or +1, we have generalized exponential and logarithm formulas to 2D quaternionic algebras Cl0;2, Cl1;1, and Cl2;0. The sectors in the multivector coefficient space, where 2D logarithm exists are found. They are related with a square root of the multivector.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43974456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-07DOI: 10.15388/namc.2022.27.26638
Nanxiang Yu, Wei Zhu
Exponential stabilization of fractional-order continuous-time dynamic systems via eventtriggered impulsive control (EIC) approach is investigated in this paper. Nonlinear and linear fractional-order continuous-time dynamic systems are studied, respectively. The impulsive instants are determined by some given event-triggering function and event-triggering condition, which are dependent on the state of the systems. Sufficient conditions on exponential stabilization for nonlinear and linear cases are presented, respectively. Moreover, the Zeno-behavior of impulsive instants is excluded. Finally, the validity of theoretical results are also illustrated by some numerical simulation examples including the synchronization control of fractional-order jerk chaotic system.
{"title":"Exponential stabilization of fractional-order continuous-time dynamic systems via event-triggered impulsive control","authors":"Nanxiang Yu, Wei Zhu","doi":"10.15388/namc.2022.27.26638","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26638","url":null,"abstract":"Exponential stabilization of fractional-order continuous-time dynamic systems via eventtriggered impulsive control (EIC) approach is investigated in this paper. Nonlinear and linear fractional-order continuous-time dynamic systems are studied, respectively. The impulsive instants are determined by some given event-triggering function and event-triggering condition, which are dependent on the state of the systems. Sufficient conditions on exponential stabilization for nonlinear and linear cases are presented, respectively. Moreover, the Zeno-behavior of impulsive instants is excluded. Finally, the validity of theoretical results are also illustrated by some numerical simulation examples including the synchronization control of fractional-order jerk chaotic system.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46535343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-05DOI: 10.15388/namc.2022.27.26623
Yiheng Wei, Jinde Cao, Chuang Li, Y. Chen
In this paper, the initial condition independence property of Grünwald–Letnikov fractional difference is revealed for the first time. For example, the solution x(k) of equation aG∇kαx(k) = f(x(k)), k > a + 1, cannot be calculated with initial condition x(a). First, the initial condition independence property is carefully investigated in both time domain and frequency domain. Afterwards, some possible schemes are formulated to make the considered system connect to initial condition. Armed with this information, the concerned property is examined on three modified Grünwald–Letnikov definitions. Finally, results from illustrative examples demonstrate that the developed schemes are sharp.
{"title":"How to empower Grünwald–Letnikov fractional difference equations with available initial condition?","authors":"Yiheng Wei, Jinde Cao, Chuang Li, Y. Chen","doi":"10.15388/namc.2022.27.26623","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26623","url":null,"abstract":"In this paper, the initial condition independence property of Grünwald–Letnikov fractional difference is revealed for the first time. For example, the solution x(k) of equation aG∇kαx(k) = f(x(k)), k > a + 1, cannot be calculated with initial condition x(a). First, the initial condition independence property is carefully investigated in both time domain and frequency domain. Afterwards, some possible schemes are formulated to make the considered system connect to initial condition. Armed with this information, the concerned property is examined on three modified Grünwald–Letnikov definitions. Finally, results from illustrative examples demonstrate that the developed schemes are sharp.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48309484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-31DOI: 10.15388/namc.2022.27.26602
Devendiran Rajkumar, A. Subramanyam Reddy
The current work deals with the pulsating flow of Au-blood micropolar nanofluid with the existence of thermal radiation and Joule heating. Micropolar fluid is addressed as blood (base fluid) and Au (gold) as a nanoparticle. The flow has been mathematically modeled, resulting in a delicate system of partial differential equations (PDEs). A perturbation technique is used to convert the PDE system into ordinary differential equations (ODEs), which are subsequently solved by using the shooting method with the Runge–Kutta fourth-order scheme. The effects of various parameters on the velocity, microrotation, temperature, and heat transfer rate of Au-blood nanofluid are graphically depicted and explored successively. The obtained findings bring out that the velocity of nanofluid decreases over a rise in the coupling parameter, magnetic field, and nanoparticle volume fractions. The temperature is reducing with an increment of radiation parameter, frequency parameter, coupling parameter, magnetic field, and volume fraction of nanoparticles. Further, the results show that the Nusselt number against frequency distribution increasing with the rising values of the Eckert number.
{"title":"Pulsating hydromagnetic flow of Au-blood micropolar nanofluid in a channel with Ohmic heating, thermal radiation and heat source/sink","authors":"Devendiran Rajkumar, A. Subramanyam Reddy","doi":"10.15388/namc.2022.27.26602","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26602","url":null,"abstract":"The current work deals with the pulsating flow of Au-blood micropolar nanofluid with the existence of thermal radiation and Joule heating. Micropolar fluid is addressed as blood (base fluid) and Au (gold) as a nanoparticle. The flow has been mathematically modeled, resulting in a delicate system of partial differential equations (PDEs). A perturbation technique is used to convert the PDE system into ordinary differential equations (ODEs), which are subsequently solved by using the shooting method with the Runge–Kutta fourth-order scheme. The effects of various parameters on the velocity, microrotation, temperature, and heat transfer rate of Au-blood nanofluid are graphically depicted and explored successively. The obtained findings bring out that the velocity of nanofluid decreases over a rise in the coupling parameter, magnetic field, and nanoparticle volume fractions. The temperature is reducing with an increment of radiation parameter, frequency parameter, coupling parameter, magnetic field, and volume fraction of nanoparticles. Further, the results show that the Nusselt number against frequency distribution increasing with the rising values of the Eckert number.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43756516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-28DOI: 10.15388/namc.2022.27.26575
Sihua Liang, Giovanni Molica Bisci, Binlin Zhang
In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problem with critical variable exponent. By using constraint variational method and quantitative deformation lemma we show the existence of one least energy solution, which is strictly larger than twice of that of any ground state solution.
{"title":"Sign-changing solutions for Kirchhoff-type problems involving variable-order fractional Laplacian and critical exponents","authors":"Sihua Liang, Giovanni Molica Bisci, Binlin Zhang","doi":"10.15388/namc.2022.27.26575","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26575","url":null,"abstract":"In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problem with critical variable exponent. By using constraint variational method and quantitative deformation lemma we show the existence of one least energy solution, which is strictly larger than twice of that of any ground state solution.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46271229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-28DOI: 10.15388/namc.2022.27.26558
Linas Litvinas
The proposed multi-objective optimization algorithm hybridizes random global search with a local refinement algorithm. The global search algorithm mimics the Bayesian multi-objective optimization algorithm. The site of current computation of the objective functions by the proposed algorithm is selected by randomized simulation of the bi-objective selection by the Bayesian-based algorithm. The advantage of the new algorithm is that it avoids the inner complexity of Bayesian algorithms. A version of the Hooke–Jeeves algorithm is adapted for the local refinement of the approximation of the Pareto front. The developed hybrid algorithm is tested under conditions previously applied to test other Bayesian algorithms so that performance could be compared. Other experiments were performed to assess the efficiency of the proposed algorithm under conditions where the previous versions of Bayesian algorithms were not appropriate because of the number of objectives and/or dimensionality of the decision space.
{"title":"A hybrid of Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems","authors":"Linas Litvinas","doi":"10.15388/namc.2022.27.26558","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26558","url":null,"abstract":"The proposed multi-objective optimization algorithm hybridizes random global search with a local refinement algorithm. The global search algorithm mimics the Bayesian multi-objective optimization algorithm. The site of current computation of the objective functions by the proposed algorithm is selected by randomized simulation of the bi-objective selection by the Bayesian-based algorithm. The advantage of the new algorithm is that it avoids the inner complexity of Bayesian algorithms. A version of the Hooke–Jeeves algorithm is adapted for the local refinement of the approximation of the Pareto front. The developed hybrid algorithm is tested under conditions previously applied to test other Bayesian algorithms so that performance could be compared. Other experiments were performed to assess the efficiency of the proposed algorithm under conditions where the previous versions of Bayesian algorithms were not appropriate because of the number of objectives and/or dimensionality of the decision space.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43499583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-16DOI: 10.15388/namc.2022.27.26483
A. Roy, Fahad Al Basir, P. Roy, A. Chatterjee
This article deals with a immunological model, which includes multiple classes of T cells, namely, the naive T cell, type I, type II and type 17 T helper cells (Th1, Th2, Th17), regulatory T cell (Treg) along with the activated natural killer cells (NK cells) and epidermal keratinocytes. In order to describe the etiology of psoriasis development, we have studied the basic mathematical properties of the model, existence and stability of the interior equilibrium. We have also derived the drug-induced mathematical model using impulse differential equation to determine the effects of combined biologics Etanercept (TNF-α inhibitor) and Fezakinumab (IL-22 monoclonal antibody) therapy considering perfect dosing during the inductive phase. We have determined the required dosing interval of both drugs to maintain the keratinocytes concentration below a threshold level. This study shows that Etanercept alone could theoretically maintain the keratinocytes level, whereas frequent dosing of Fezakinumab alone may not be enough to control the hyper-proliferation of keratinocytes. Furthermore, combination of the drugs with perfect dosing has the noticeable effect on keratinocytes dynamics, which may be suitable therapeutic approaches for treatment of psoriasis.
{"title":"A model analysis to measure the adherence of Etanercept and Fezakinumab therapy for the treatment of psoriasis","authors":"A. Roy, Fahad Al Basir, P. Roy, A. Chatterjee","doi":"10.15388/namc.2022.27.26483","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26483","url":null,"abstract":"This article deals with a immunological model, which includes multiple classes of T cells, namely, the naive T cell, type I, type II and type 17 T helper cells (Th1, Th2, Th17), regulatory T cell (Treg) along with the activated natural killer cells (NK cells) and epidermal keratinocytes. In order to describe the etiology of psoriasis development, we have studied the basic mathematical properties of the model, existence and stability of the interior equilibrium. We have also derived the drug-induced mathematical model using impulse differential equation to determine the effects of combined biologics Etanercept (TNF-α inhibitor) and Fezakinumab (IL-22 monoclonal antibody) therapy considering perfect dosing during the inductive phase. We have determined the required dosing interval of both drugs to maintain the keratinocytes concentration below a threshold level. This study shows that Etanercept alone could theoretically maintain the keratinocytes level, whereas frequent dosing of Fezakinumab alone may not be enough to control the hyper-proliferation of keratinocytes. Furthermore, combination of the drugs with perfect dosing has the noticeable effect on keratinocytes dynamics, which may be suitable therapeutic approaches for treatment of psoriasis.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45352423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-25DOI: 10.15388/namc.2022.27.26407
Rohit Patel, A. Shukla, J. Nieto, V. Vijayakumar, S. Jadon
The objective of our paper is to investigate the optimal control of semilinear population dynamics system with diffusion using semigroup theory. The semilinear population dynamical model with the nonlocal birth process is transformed into a standard abstract semilinear control system by identifying the state, control, and the corresponding function spaces. The state and control spaces are assumed to be Hilbert spaces. The semigroup theory is developed from the properties of the population operators and Laplacian operators. Then the optimal control results of the system are obtained using the C0-semigroup approach, fixed point theorem, and some other simple conditions on the nonlinear term as well as on operators involved in the model.
{"title":"New discussion concerning to optimal control for semilinear population dynamics system in Hilbert spaces","authors":"Rohit Patel, A. Shukla, J. Nieto, V. Vijayakumar, S. Jadon","doi":"10.15388/namc.2022.27.26407","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26407","url":null,"abstract":"The objective of our paper is to investigate the optimal control of semilinear population dynamics system with diffusion using semigroup theory. The semilinear population dynamical model with the nonlocal birth process is transformed into a standard abstract semilinear control system by identifying the state, control, and the corresponding function spaces. The state and control spaces are assumed to be Hilbert spaces. The semigroup theory is developed from the properties of the population operators and Laplacian operators. Then the optimal control results of the system are obtained using the C0-semigroup approach, fixed point theorem, and some other simple conditions on the nonlinear term as well as on operators involved in the model.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45357465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-23DOI: 10.15388/namc.2022.27.26374
L. Akinyemi, M. Mirzazadeh, K. Hosseini
We analytically study the exact solitary wave solutions of the perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index, which describes the propagation of pulses of various types in optical fiber. We apply three efficient and reliable schemes, specifically, the simple equation method, the (G'/G)-expansion method, and the new Kudryashov method. These approaches lead to a range of solitons and other solutions comprising of the bright solitons, dark solitons, singular solitons, periodic, rational, and exponential solutions. These solutions are also presented graphically. Furthermore, all obtained solutions are verified by symbolic computations.
{"title":"Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index","authors":"L. Akinyemi, M. Mirzazadeh, K. Hosseini","doi":"10.15388/namc.2022.27.26374","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26374","url":null,"abstract":"We analytically study the exact solitary wave solutions of the perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index, which describes the propagation of pulses of various types in optical fiber. We apply three efficient and reliable schemes, specifically, the simple equation method, the (G'/G)-expansion method, and the new Kudryashov method. These approaches lead to a range of solitons and other solutions comprising of the bright solitons, dark solitons, singular solitons, periodic, rational, and exponential solutions. These solutions are also presented graphically. Furthermore, all obtained solutions are verified by symbolic computations.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45443471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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