Mathematics And Statistics - Research Publications

Permanent URI for this collectionhttps://kr.cup.edu.in/handle/32116/47

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A note on "A fuzzy approach to transport optimization problem"
(Springer New York LLC, 2016) Sidhu, Sukhpreet Kaur; Kumar, Amit; Kaur, Amarpreet
Sudhagar and Ganesan (Optim Eng, 2012, doi:10.1007/s11081-012-9202-6) proposed an approach to find the fuzzy optimal solution of such fuzzy transportation problems in which all the parameters are represented by fuzzy numbers. In this note, it is pointed out that the authors have used some mathematical incorrect assumptions in their proposed method. ? 2015, Springer Science+Business Media New York.
Solitons and other solutions to Wu–Zhang system
(Vilnius University, 2017) Mirzazadeha, Mohammad; Ekicib, Mehmet; Eslamic, Mostafa; Krishnand, Edamana Vasudevan; Kumar, Sachin; Biswas, Anjan
This paper addresses Wu–Zhang system to study dispersive long waves. The extended trial equation method extracts solitary waves, shock waves, and singular solitary waves solutions. Subsequently, Lie group formalism is also applied to derive symmetries of the Wu–Zhang system, and the derived ordinary differential equations are further analyzed to retrieve exact solutions are obtained. Finally, implementation of mapping method secures additional exact solutions.
Space–time fractional nonlinear partial differential equations: symmetry analysis and conservation laws
(Springer, 2017) Singla, Komal; Gupta, R. K.
The symmetry method is developed to study space–time fractional nonlinear partial differential equations. Also, the Noether operators are extended for determining the conservation laws by application to some physically significant space–time fractional nonlinear partial differential equations.
Nonclassical symmetries and similarity solutions of variable coefficient coupled KdV system using compatibility method
(Springer Netherlands, 2017) Gupta, R. K.; Singh, Manjit; Gupta, R.K.; Singh, M.
The variable coefficient KdV system is investigated for nonclassical symmetries using compatibility method, and more general symmetries are reported. Several inequivalent reductions are obtained using optimal system of subalgebras, and using well-known methodologies, several traveling wave solutions are also obtained for every reduction. ? 2016, Springer Science+Business Media Dordrecht.
Invariant solutions of Biswas-Milovic equation
(Springer Netherlands, 2017) Kumar, Sachin
The Biswas-Milovic equation in generalized form and with power law nonlinearity is analyzed for Lie symmetries. The classical Lie group method is applied to derive symmetries of this equation, and the ordinary differential equations deduced are further studied; and some exact solutions are obtained. ? 2016, Springer Science+Business Media Dordrecht.
Comment on “Lie symmetries and group classification of a class of time fractional evolution systems” [J. Math. Phys. 56, 123504 (2015)]
(Springer, 2017) Singla, Komal; Gupta, R. K.
In this article, the prolongation formulae proposed in Huang and Shen [J. Math. Phys. 56, 123504 (2015)] for the analysis of time fractional systems of are proved incomplete and the required correct prolongation operators are suggested. With the help of some examples, the efficiency of the operators introduced in this study is illustrated.
On Kropina-Randers change of mth-root Finsler metric
(Pushpa Publishing House, 2017) Shanker, G.; Baby, S.A.
In the present paper, we consider the Kropina-Randers change of mth root Finsler metric. Firstly, we find the fundamental metric tensors of the Kropina-Randers transformed mth root Finsler metric, and then the necessary and sufficient condition under which the Kropina-Randers change of the mth root Finsler metric is locally dually flat. Further, we prove that the Kropina-Randers change of mth root Finsler metric is locally projectively flat if and only if it is locally Minkowskian. ? 2017 Pushpa Publishing House, Allahabad, India.
Symmetry analysis, explicit power series solutions and conservation laws of space-time fractional variant Boussinesq system
(Springer, 2018) Baljinder Kour; Sachin Kumar
In 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.
Four-dimensional conformally flat Berwald and Landsberg spaces
(Informatics Publishing Limited and The Indian Mathematical Society, 2018) Shanker, G.
The problem of conformal transformation and conformal atness of Finsler spaces has been studied in [6], [16], [17], [20], [21]. Recently, Prasad et. al [19] have studied three dimensional conformally at Landsberg and Berwald spaces and have obtained some important results. The purpose of the present paper is to extend the idea of conformal change to four dimensional Finsler spaces and find the suitable conditions under which a four dimensional conformally at Landsberg space becomes a Berwald space. ? 2018 Indian Mathematical Society.
Invariants of Generalized Fifth Order Non-Linear Partial Differential Equation
(IntechOpen, 2018) Kumar, Sachin
The 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.
Exact Solutions of Some Complex Non-Linear Equations," Lecture Notes in Engineering and Computer Science
(Newswood Limited, 2018) Kumar, Sachin
Exact 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.
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]
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.
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.
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.
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.
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).
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.
Invariant Analysis for Space�Time Fractional Three-Field Kaup�Boussinesq Equations
(Springer Science and Business Media Deutschland GmbH, 2020-09-30T00:00:00) Kaur, Jaskiran; Kumar Gupta, Rajesh; Kumar, Sachin
Symmetries of the nonlinear fractional�differential equations are an interesting�and important topic. In this paper, space�time fractional three-field Kaup�Boussinesq equations with Riemann�Liouville fractional derivative are studied for invariant analysis. Symmetries are obtained by using classical Lie�s symmetry approach. Using obtained symmetries, the governing equations reduce to system of fractional ordinary differential equations which contains left and right-sided Erde� lyi- Kober (EK) fractional operators. � 2021, Springer Nature Singapore Pte Ltd.
A malaria model with Caputo-Fabrizio and Atangana-Baleanu derivatives
(World Scientific, 2020-11-02T00:00:00) Abboubakar, Hamadjam; Kumar, Pushpendra; Rangaig, Norodin A.; Kumar, Sachin
In this paper, we study two fractional models in the Caputo-Fabrizio sense and Atangana-Baleanu sense, in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered. Using Lyapunov theory, we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model, and the fractional models, whenever the basic reproduction number R0 is greater than one. By using fixed point theory, we prove existence, and conditions of the uniqueness of solutions, as well as the stability and convergence of numerical schemes. Numerical simulations for both models, using fractional Euler method and Adams-Bashforth method, respectively, are provided to confirm the effectiveness of used approximation methods for different values of the fractional-order ?. � 2021 World Scientific Publishing Company.