Dr. Manoj Kumar
@bmu.ac.in
Professor and Head, Department of Mathematics, Faculty of Sciences
Baba Mastnath University, Rohtak
Experience of more than 20 years in teaching and Ph.D. in Mathematics
EDUCATION
Ph.D. in Mathematics
RESEARCH, TEACHING, or OTHER INTERESTS
Mathematics, Applied Mathematics
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Preeti Bhardwaj and Manoj Kumar
AIP Publishing
Deepika and Manoj Kumar
AIP Publishing
Manoj Kumar, Ozgur Ege, Vinit Mor, Pankaj Kumar, and Manuel De la Sen
Elsevier BV
Pankaj and Manoj Kumar
Sociedade Paranaense de Matemática
In this paper, we introduce the weak ()-Jaggi type contraction. The existence and uniqueness of fixed point for such contraction is investigated. It is very helpful in extending the existing results of corresponding literature. In addition, we also provide an example in support of our theorem.
Shruti Goel, Vandana Gupta, and Manoj Kumar
World Scientific Pub Co Pte Ltd
In this paper, we discuss the reflection and refraction of an incident P wave or [Formula: see text] wave at the interface of a plane. The plane, which is divided into two halves, is an elastic medium [Formula: see text] having an incident wave and a thermoelastic diffusion medium [Formula: see text] with TPLT (i.e., three-phase-lag thermal) and TPLD (i.e., three-phase-lag diffusion) models. It has been noticed that two waves are reflected and four are refracted in an isotropic thermoelastic diffusion medium. Out of the four refracted waves, three are longitudinal waves: a quasi-longitudinal wave [Formula: see text] a quasi-mass diffusion wave [Formula: see text], a quasi-thermal wave [Formula: see text] and one is a transverse wave [Formula: see text]. If we consider the above waves first, the amplitude and energy ratio are calculated by using the surface boundary conditions and then graphically represented to compare the change in energy and amplitude ratio with the change in incident angle for three particular cases. The conservation of energy is depicted by verifying that all the energy sums up to unity. The considered problem has its application in earthquake engineering, astronautics, rocket engineering, seismology and many more engineering areas.
Sapna Pandit, Pooja Verma, Manoj Kumar, and Poonam
Emerald
PurposeThis article offered two meshfree algorithms, namely the local radial basis functions-finite difference (LRBF-FD) approximation and local radial basis functions-differential quadrature method (LRBF-DQM) to simulate the multidimensional hyperbolic wave models and work is an extension of Jiwari (2015).Design/methodology/approachIn the evolvement of the first algorithm, the time derivative is discretized by the forward FD scheme and the Crank-Nicolson scheme is used for the rest of the terms. After that, the LRBF-FD approximation is used for spatial discretization and quasi-linearization process for linearization of the problem. Finally, the obtained linear system is solved by the LU decomposition method. In the development of the second algorithm, semi-discretization in space is done via LRBF-DQM and then an explicit RK4 is used for fully discretization in time.FindingsFor simulation purposes, some 1D and 2D wave models are pondered to instigate the chastity and competence of the developed algorithms.Originality/valueThe developed algorithms are novel for the multidimensional hyperbolic wave models. Also, the stability analysis of the second algorithm is a new work for these types of model.
Pooja Verma, Sapna Pandit, Manoj Kumar, Vikas Kumar, and Poonam Poonam
IOP Publishing
Abstract The current study is dedicated to solving the time-fractional (2+1)-dimensional Navier–Stokes model. The model has wide applications in blood flow, in the design of power stations, weather prediction, ocean currents, water flow in a pipe, air flow around the aircraft wings, the analysis of pollution, and many other areas of engineering. The Lie symmetry approach is applied to the governed time-fractional equation to fulfill this need. In the direction of exact solutions of the time-fractional equation first of all invariance condition is obtained in the presence of the Lie group. Consequently, infinitesimals are obtained with the help of the invariant condition. Moreover, these infinitesimals are utilized to obtain the subalgebras. Further, under each subalgebras similarity variables and similarity solutions are obtained which are used to find the reduced equations. These reduced equations are solved for exact solutions. The solutions of the reduced equations are further used to find the exact solutions of the main time-fractional (2+1)-dimensional Navier–Stokes equation with the help of similarity solutions under each subalgebra.
Manoj Kumar, Pankaj Kumar, Ali Mutlu, Rajagopalan Ramaswamy, Ola A. Ashour Abdelnaby, and Stojan Radenović
MDPI AG
Here, we shall introduce the new notion of C*-algebra valued bipolar b-metric spaces as a generalization of usual metric spaces, C*-algebra valued metric space, b-metric spaces. In the above-mentioned spaces, we shall define (αA−ψA) contractions and prove some fixed point theorems for these contractions. Some existing results from the literature are also proved by using our main results. As an application Ulam–Hyers stability and well-posedness of fixed point problems are also discussed. Some examples are also given to illustrate our results.
Preeti ., Manoj Kumar, and Poonam .
Ramanujan Society of Mathematics and Mathematical Sciences
This manuscript consists a common fixed point result for four weakly compatible self-maps ˆ P, ˆ Q, ˆ S, ˆ T on a metric space (M, d∗) satisfying the following contractive inequality of integral type: Z d∗( ˆ Tμ, ˆ Sν) 0 ξ(t)dt ≤ β(d∗(μ, ν)) Z Δ1(μ,ν) 0 ξ(t)dt, where (ξ, β) ∈ ξ1 × ξ3 and for all μ, ν in M. Δ1(μ, ν) = max{d∗( ˆ Tμ, ˆ Sν), d∗( ˆ Tμ, ˆ Pμ), d∗( ˆ Sν, ˆ Qν), 1 2 [d∗( ˆ Pμ, ˆ Sν) + d∗( ˆ Qν, ˆ Tμ)], d∗( ˆ Pμ, ˆ Tμ).d∗( ˆ Qν, ˆ Sν) 1 + d∗( ˆ Tμ, ˆ Sν) , d∗( ˆ Pμ, ˆ Sν).d∗( ˆ Qν, ˆ Tμ) 1 + d∗( ˆ Tμ, ˆ Sν) , d∗( ˆ Tμ, ˆ Pμ)[ 1 + d∗( ˆ Tμ, ˆ Qν) + d∗( ˆ Sν, ˆ Pμ) 1 + d∗( ˆ Tμ, ˆ Pμ) + d∗( ˆ Sν, ˆ Qν) ]}. 150 South East Asian J. of Mathematics and Mathematical Sciences Also, some common fixed point results for the above mentioned weakly compatible self - maps along with E.A. property and (CLR) property are proved. A suitable illustrative example is also provided to support our result
Manoj Kumar, Pankaj Kumar, Rajagopalan Ramaswamy, Ola A. Ashour Abdelnaby, Amr Elsonbaty, and Stojan Radenović
MDPI AG
In this paper, we introduce the new notion of contravariant (α−ψ) Meir–Keeler contractive mappings by defining α-orbital admissible mappings and covariant Meir–Keeler contraction in bipolar metric spaces. We prove fixed point theorems for these contractions and also provide some corollaries of main results. An example is also be given in support of our main result. In the end, we also solve an integral equation using our result.
Pooja Verma, Vikas Kumar, Manoj Kumar, and Poonam
World Scientific Pub Co Pte Ltd
In this work, Lie symmetry analysis method is utilized to find the complex soliton solutions of the perturbed Fokas–Lenells equation. In this direction, first of all, we obtained the infinitesimals of the Fokas–Lenells equation with the help of the Lie symmetry method. After that, we reduced the Fokas–Lenells equation into the highly nonlinear system of an ordinary differential equation. Consequently, with the application of suitable back transformation, complex solitons are formulated for the Fokas–Lenells equation in trigonometric, hyperbolic and exponential functions. Finally, in this work, conditions of stability and instability are discussed with the aid of baseband modulation instability.
Rashmi Sharma and Manoj Kumar
Ramanujan Society of Mathematics and Mathematical Sciences
In this paper, we introduce new notions of α0−(ψ0,g0)- proximal contraction of Type-I and Type-II and modified α0 − (ψ0,g0)- proximal contraction. In the setting of these notions, we prove certain fixed point theorems in metric space. Additionally, a few applications are provided to show how the results can be used.
Amit Duhan, Manoj Kumar, Savita Rathee, and Monika Swami
SCIK Publishing Corporation
In this paper, we find the best proximity point in G-metric spaces for G-generalized ζ-β-T contraction mappings and verify the existence and uniqueness of the best proximity point in the complete G metric space using the idea of an approximatively compact set. In addition, an example is provided to illustrate the outcome.
A Ashish, M Monia, Manoj Kumar, K Khamosh, and A.K. Malik
National Library of Serbia
The difference and differential equations have played an eminent part in nonlinear dynamics systems, but in the last two decades one-dimensional difference maps are considered in the forefront of nonlinear systems and the optimization of transportation problems. In the nineteenth century, the nonlinear systems have paved a significant role in analyzing nonlinear phenomena using discrete and continuous time interval. Therefore, it is used in every branch of science such as physics, chemistry, biology, computer science, mathematics, neural networks, traffic control models, etc. This paper deals with the maximum Lyapunov exponent property of the nonlinear dynamical systems using Euler?s numerical algorithm. The presents experimental as well as numerical analysis using time-series diagrams and Lyapunov functional plots. Moreover, due to the strongest property of Lyapunov exponent in nonlinear system it may have some application in the optimization of transportation models.
Priya Goel, Manoj Kumar, Dimple Singh, and Kamal Kumar
Hindawi Limited
In this manuscript, we have established relation-theoretic version of some common fixed point results in metric space for generalized β − ϕ − Z -contractive pair of mappings furnished with an arbitrary binary relation R . Recently, the concept of binary relation is well known leading trend in fixed point theory. Our results extend and unify several fixed point theorems present in the literature. An illustrative example is given to support our main theorem. Finally, we exploit our main result for proving existence and uniqueness results to established the solution of a fractional differential equation of Caputo type.
Narinder Kumar and M. Kumar
SCIK Publishing Corporation
In this paper, with the aid of simulation mapping η ∶ [0, ∞) × [0, ∞) → R, we prove some Lemmas and fixed point result for generalized Z − contraction of the mapping g ∶ X → X satisfying the following conditions: η(G(gx, gy, gz), M(x, y, z)) ≥ 0, for all x, y, z ∈ X, where M(x, y, z) = max {G(x, gy, gy), G(y, gx, gx), G(y, gz, gz), G(z, gy, gy), G(z, gx, gx), G(x, gz, gz)}. and (X, G) is a G − metric space. An example is also given to support our results.
Manoj Kumar and Sahil Arora
Sociedade Paranaense de Matematica
In this paper, we introduce new notions of generalized F-contractions of type(S) and type(M) in G-metric spaces. Some common fixed point theorems are proved using these notions. A suitable example is also provided to support our results.