Nonlinear Analysis: Modelling and Control http://www.journals.vu.lt/nonlinear-analysis <p>Founded in 1997. Journal provides a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature.&nbsp;</p> Vilnius University Press en-US Nonlinear Analysis: Modelling and Control 1392-5113 <p>Please read the Copyright Notice in&nbsp;<a href="http://www.zurnalai.vu.lt/acta-paedagogica-vilnensia/journalpolicy">Journal Policy</a>.&nbsp;</p> Nonlinear studies on the effect of non-uniform heat generation/absorption on hydromagnetic flow of nanofluid over a vertical plate http://www.journals.vu.lt/nonlinear-analysis/article/view/13406 <p>The analytical and numerical studies are performed to investigate the non-uniform heat generation/absorption effect on the boundary layer flow of an incompressible, electrically conducting nanofluid over a vertical plate in the presence of thermal radiation. The highly nonlinear governing equations along with the boundary conditions are converted into ordinary differential equations by appropriate similarity transformations. The transformed highly nonlinear ordinary differential equations are solved both analytically and numerically using homotopy analysis method and fourth order Runge–Kutta method with shooting technique respectively, for the various values of physical parameters. The results show that the presence of both space and temperature dependent heat generation enhances the velocity and temperature profiles and reduces the solid volume fraction of nanofluid profile. Comparison between present analytical and numerical results is found to be good.</p> Abdul Kafoor Abdul Hakeem Bhose Ganga Sait Mohamed Yusuff Ansari Nagaraj Vishnu Ganesh Mohammad Mansur Rahman ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-01-20 2017-01-20 22 1 1 16 10.15388/NA.2017.1.1 Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem http://www.journals.vu.lt/nonlinear-analysis/article/view/13407 <p>An existence theorem for Volterra-type integral inclusion is establish in&nbsp;<em>b</em>-metric spaces. We first introduce two new&nbsp;<em>F</em>-contractions of Hardy–Rogers type and then establish fixed point theorems for these contractions in the setting of&nbsp;<em>b</em>-metric spaces. Finally, we apply our fixed point theorem to prove the existence theorem for Volterra-type integral inclusion. We also provide an example to show that our fixed point theorem is a proper generalization of a&nbsp;recent fixed point theorem by Cosentino et al.</p> Muhammad Usman Ali Tayyab Kamran Mihai Postolache ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-01-20 2017-01-20 22 1 17 30 10.15388/NA.2017.1.2 Bifurcation analysis for a singular differential system with two parameters via to topological degree theory http://www.journals.vu.lt/nonlinear-analysis/article/view/13408 <p>Based on the relation between Leray–Schauder degree and a pair of strict lower and upper solutions, we focus on the bifurcation analysis for a singular differential system with two parameters, explicit bifurcation points for relative parameters are obtained by using the property of solution for the akin systems and topological degree theory.</p> Lishan Liu Fenglong Sun Xinguang Zhang Yonghong Wu ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-01-20 2017-01-20 22 1 31 50 10.15388/NA.2017.1.3 Rational g-ω-weak contractions and fixed point theorems in 0-σ-complete metric-like spaces http://www.journals.vu.lt/nonlinear-analysis/article/view/13409 <p>We bring in the notion of rational&nbsp;<em>g-ω</em>-weak contractions in metric-like spaces and demonstrate common fixed point results for such mappings in 0-<em>σ</em>-complete metric-like spaces. Examples are given to support the usability of our results and to show that they are improvements of some known ones. An application to second-order differential equations is presented in the final section.</p> Hemant Kumar Nashine Anita Gupta Zoran Kadelburg ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-01-20 2017-01-20 22 1 51 63 10.15388/NA.2017.1.4 Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay http://www.journals.vu.lt/nonlinear-analysis/article/view/13410 <p>In this paper, deterministic and stochastic SEIRI epidemic models featuring a distributed latent period and general, unspecified nonlinear incidence and growth rates for the susceptible class are proposed and investigated from a stability viewpoint. By applying Lyapunov–LaSalle invariance principle, we first obtain sufficient conditions for the global stability of equilibria of the deterministic model. On the basis of this result, we subsequently derive sufficient conditions for asymptotic stability of the stochastic model. Finally, numerical simulations are given to illustrate the previously obtained theoretical framework.</p> Hong Zhang Juan Xia Paul Georgescu ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-01-20 2017-01-20 22 1 64 83 10.15388/NA.2017.1.5 Fixed point teorems for multivalued maps via new auxiliary function http://www.journals.vu.lt/nonlinear-analysis/article/view/13411 <p>We introduce a contractive condition involving new auxiliary function and prove a&nbsp;fixed point theorem for closed multivalued maps on complete metric spaces. An example and an application to integral equation are given in support of our findings.</p> Muhammad Usman Ali Calogero Vetro ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-01-20 2017-01-20 22 1 84 98 10.15388/NA.2017.1.6 Existence of positive solutions for a singular fractional boundary value problem http://www.journals.vu.lt/nonlinear-analysis/article/view/13412 <p>We study the existence of positive solutions for a nonlinear Riemann–Liouville fractional differential equation with a sign-changing nonlinearity, subject to multi-point fractional boundary conditions.</p> Johnny Henderson Rodica Luca ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-01-20 2017-01-20 22 1 99 114 10.15388/NA.2017.1.7 Investigation of symmetric non-spherical particle shapes by applying low-resolution spherical harmonics http://www.journals.vu.lt/nonlinear-analysis/article/view/13413 <p>The issue of mathematical modelling of non-spherical shapes of particles is considered. Thus, application of the spherical harmonics (SH) technique in modelling the simplest symmetric star-shaped particles is demonstrated by applying low-resolution functions. The investigation was restricted to a circular cylinder and a rectangular parallelepiped, geometrically primitive, but widespread oblate industrial shapes. The modelling quality was studied by considering selected error norms and the most important integral characteristics of a particle geometry, including the surface area and volume. The presented results discovered new features of the spherical harmonic technique and enhanced understanding of their applicability to describe non-spherical shapes.</p> Urtė Radvilaitė Rimantas Kačianauskas Dainius Rusakevičius ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-01-20 2017-01-20 22 1 115 133 10.15388/NA.2017.1.8 On economic-technological optimization of high-voltage electric cables http://www.journals.vu.lt/nonlinear-analysis/article/view/13414 <p>In this paper, mathematical modelling of high voltage cables for power transmission line design is presented. The Finite Volume Method (FVM) is used to approximate the developed mathematical model (a system of nonlinear multi-physic differential equations) and OpenFOAM (Open source Field Operation And Manipulation) tool is used to implement the obtained parallel finite volume schemes. In order to optimize the design of power lines with respect to technological parameters, different cases of nonstationary load dynamics are investigated and the influence of system nonlinearity and external day, month and years periodical boundary conditions and the source function regimes are simulated. The main aim of this paper is to include into the mathematical model also economic requirements and to optimize sizes of cables with respect to both technologic and economic requirements. Numerical algorithms targeted to solve PDE-constrained optimization problems are developed. Results of computational experiments are presented.</p> Mečislavas Meilūnas Audrius Ilgevičius Olga Suboč Gerda Jankevičiūtė Raimondas Čiegis ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-01-20 2017-01-20 22 1 134 146 10.15388/NA.2017.1.9