Department Of Mathematics And Statistics
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Item On new symmetry, series solution and conservation laws of nonlinear coupled Higgs field equation(Springer, 2020) Kumari, P; Gupta, R.K; Kumar, S.The work presents systematic investigations on invariant analysis and the analytic solution of the second order Higgs equation. On employing Lie classical approach, new symmetry and the corresponding reduction of the system are obtained. Explicit convergent infinite series solution of the reduced system is obtained. Local conservation laws of the system are derived by the multiplier approach. 2020, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.Item Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations(Springer, 2020) Bedi, P; Kumar, A; Abdeljawad, T; Khan, A.In this paper, we investigate the existence of mild solutions for neutral Hilfer fractional evolution equations with noninstantaneous impulsive conditions in a Banach space. We obtain the existence results by applying the theory of resolvent operator functions, Hausdorff measure of noncompactness, and Sadovskii's fixed point theorem. We also present an example to show the validity of obtained results. 2020, The Author(s).Item On S -curvature of a homogeneous Finsler space with square metric(World Scientific Publishing Co. Pte Ltd, 2020) Shanker G.; Rani S.The study of curvature properties of homogeneous Finsler spaces with (?,?)-metrics is one of the central problems in Riemann-Finsler geometry. In this paper, the existence of invariant vector fields on a homogeneous Finsler space with square metric is proved. Further, an explicit formula for S-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of S-curvature, the mean Berwald curvature of aforesaid (?,?)-metric is calculated.Item Comment on “Time fractional third-order variant Boussinesq system: Symmetry analysis, explicit solutions, conservation laws and numerical approximations” by Fairouz Tchier et al.(Springer Verlag, 2019) Kour B.; Kumar S.[No abstract available]Item Space time fractional Drinfel'd-Sokolov-Wilson system with time-dependent variable coefficients: Symmetry analysis, power series solutions and conservation laws(Springer Verlag, 2019) Kour B.; Kumar S.In this work we aim to apply the Lie-symmetry method via the Riemann-Liouville fractional derivative based on continuous group of transformations to examine the symmetry reduction of space time fractional Drinfel'd-Sokolov-Wilson (DSW) system with time-dependent variable coefficients. The reduced Nonlinear fractional ordinary differential equations (NLFODEs) with variable coefficients are further studied for the exact solution by using the power series method. The exact solutions obtained in form of power series and their convergence show the accuracy and efficiency of the proposed method, which is simple and accurate in comparison to other methods to find the exact solution of nonlinear fractional partial differential equations (NLFPDEs). Also, the new conservation theorem and Noether's operators are used to construct conservation laws of the governing system.Item Dispersion analysis and improved F-expansion method for space–time fractional differential equations(Springer, 2019) Kaur, B; Gupta, R.K.In this article, an improved F-expansion method with the Riccati equation is suggested for space–time fractional differential equations for exact solutions. The fractional complex transformation is used to convert the space–time fractional differential equations into ordinary differential equations. The application of the method is described by solving space–time fractional potential Yu–Toda–Sasa–Fukuyama equation, and the solutions of the equation are successfully established in terms of the hyperbolic, trigonometric and rational types of functions. The graphical analysis describes the effect of fractional orders α, β, γ, δ of time and space derivatives, respectively, on the wave profile of solutions. The dispersion relation is obtained using the linear analysis, and it shows that waves follow anomalous or normal dispersion depending upon space or time fractional-order values. © 2019, Springer Nature B.V.Item On explicit exact solutions of variable-coefficient time-fractional generalized fifth-order Korteweg-de Vries equation(Springer, 2019) Gupta, R.K; Kaur, J.We investigate the variable-coefficient time-fractional generalized fifth-order Korteweg-de Vries equation for admissible forms of the variable coefficients under the condition of invariance, and derive certain explicit exact solutions for the reduced ordinary differential equations of fractional order. © 2019, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.Item Symmetry analysis, explicit power series solutions and conservation laws of space-time fractional variant Boussinesq system(Springer, 2018) Baljinder Kour; Sachin KumarIn this study, the classical Lie symmetry method is successfully applied to investigate the symmetries of the space-time fractional variant Boussinesq system which was introduced as a model of water waves. With the help of the obtained symmetries, the governing system is reduced into the system of nonlinear fractional ordinary differential equations (NLFODEs) which contains Erdèlyi-Kober fractional differential operators via Riemann-Liouville fractional derivative. The system is also studied for the explicit power series solution. The obtained power series solution is further examined for the convergence. The conservation laws of the governing system are constructed by using the new conservation theorem and generalization of the Noether operators. The numerical approximation for the fractional system is also found by using the residual power series method (RSPM). Some figures are also presented to explain the physical understanding for both explicit and approximate solutions.Item Invariants of Generalized Fifth Order Non-Linear Partial Differential Equation(IntechOpen, 2018) Kumar, SachinThe fifth order non-linear partial differential equation in generalized form is analyzed for Lie symmetries. The classical Lie group method is performed to derive similarity variables of this equation and the ordinary differential equations (ODEs) are deduced. These ordinary differential equations are further studied and some exact solutions are obtained.Item Exact Solutions of Some Complex Non-Linear Equations," Lecture Notes in Engineering and Computer Science(Newswood Limited, 2018) Kumar, SachinExact solutions of the coupled Higgs and Maccari system are obtained. Travelling wave solutions of coupled Higgs equation and Maccari system in the form of Jacobi’s elliptical functions are presented.