Mathematics, Applied Mathematics, Modeling and Simulation, General Physics and Astronomy
103
Scopus Publications
1385
Scholar Citations
23
Scholar h-index
48
Scholar i10-index
Scopus Publications
Analysis of Basins of Attraction in the Pseudo-Newtonian Photogravitational Restricted Four-Body Problem with Asteroid Belt Effects Vinay Kumar, Rajiv Aggarwal, Nitesh Kumar Kinematics and Physics of Celestial Bodies, 2026 In this study, we examine the convergence behavior of the Newton–Raphson basins of convergence in relation to the equilibrium points serving as attractors within the framework of the pseudo-Newtonian planar circular restricted four-body problem. This model accounts for the effects of both radiation pressure and the presence of a circular asteroid belt. Our focus lies on determining the positions and assessing the stability of these equilibrium points as the transition parameter, denoted by $$\epsilon $$ , is varied across the range [0, 1]. By employing a multivariate form of the Newton–Raphson iterative algorithm, we draw the basins of convergence across selected two-dimensional planes. A thorough numerical analysis is carried out to illustrate how changes in the transition parameter influence the structure and geometry of these convergence regions. Furthermore, we examine the relationship between the spatial extent of the attraction basins and the number of iterations needed to reach convergence. The results suggest that the behavior of these regions is complex yet deeply engaging, offering rich insights into the dynamics of the system.
Mathematical model for Buruli ulcer and HIV co-infection with optimal control strategy Ravi Kumar, Rajiv Aggarwal, Tanvi International Journal of Biomathematics, 2026 In this paper, we investigate the co-infection dynamics of HIV/AIDS and Buruli ulcer, incorporating prevention and treatment strategies for both diseases. The study begins by formulating a co-infection model and separately investigating the HIV and Buruli ulcer sub-models. The basic reproduction numbers for each disease are computed and demonstrate that both sub-models have two equilibrium points, namely, the disease-free equilibrium point and the unique endemic equilibrium point. For both sub-models, the disease-free equilibrium is proven to be both locally as well as globally asymptotically stable when the corresponding reproduction number is less than one, whereas the endemic equilibrium exists when the respective basic reproduction number exceeds one. The full HIV-Buruli ulcer co-infection model is further analyzed, and optimal control analysis is conducted using Pontryagin’s Maximum Principle to minimize the number of infected individuals and the costs associated with prevention and treatment efforts. Numerical simulations are performed with various combinations of control efforts, highlighting the importance of enhanced prevention alongside treatment to reduce the co-infection rates. The results emphasize that both prevention and treatment are critical for effectively controlling the spread of HIV and Buruli ulcer co-infection in the population.
Comparison of Analytical and Numerical Methods to Solve Boundary-Layer Natural Convection Problem for Various Prandtl Number Fluids Durgesh Kushawaha, Sushil Yadav, Rajiv Aggarwal Heat Transfer, 2025 Semianalytical approaches such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM), as well as the Numerical Method, are investigated in this study to solve the boundary‐layer natural convection problem for various Prandlt number fluids on a horizontal flat plate. Nonlinear partial differential expressions can be incorporated into the ordinary differential framework by applying appropriate transformations. The purpose of this study is to show how analytical solutions to heat transfer problems are more versatile and broadly applicable. The results of the analytical solutions are compared with numerical solutions, revealing a high level of approximation accuracy. The numerical findings clearly imply that the analytical techniques can produce accurate numerical solutions for nonlinear differential equations. We analyze the temperature distribution, velocity, and flow field under various conditions. The study found that temperature patterns, velocity distribution, and flow dynamics are all improved by raising the Prandtl numbers. As a result, the thickness of the boundary layer is significantly reduced, leading to an enhanced heat transfer rate at the moving surface. This reduction in boundary‐layer thickness contributes to a more efficient convection process. The study further highlights that the HPM and the VIM both offer highly accurate approximations for solving nonlinear differential equations related to boundary‐layer flow and heat transfer. Among these methods, HPM was found to provide a higher level of precision compared with VIM.
A fractional order age-structured model to study the effect of social awareness on alcohol consumption Ashutosh Rajput, Rajiv Aggarwal Physica Scripta, 2025 Alcohol misuse is a widespread societal issue that transcends class boundaries and significantly influencing various facets of life. Accordingly, we have developed a nonlinear mathematical model to explore alcohol consumption, incorporating the novel fractional-order derivative in the Caputo sense to determine the impact of memory effects on drinking behavior. The model examines the influence of adult drinking habits on the youth generation’s drinking habits as well as the role of social and media-driven awareness in shaping this phenomenon. The study has calculated the basic reproduction numbers for both youth and adult populations, which serve as measures of the contagiousness of alcohol consumption. The study has determined an alcohol-free equilibrium point that is locally stable when both reproduction numbers are below one. However, if either reproduction number exceeds one, an additional alcohol-persistence equilibrium point emerges, indicating the potential for a backward bifurcation in the model. Numerical findings suggest that increasing the memory effect by decreasing the value of α can significantly reduce the number of drinkers. Additionally, it is observed that if adult potential drinkers abstain from alcohol and create an alcohol-free environment for the youth, the drinking population can be substantially diminished. Therefore, a combined effort from both the youth and adult populations is essential to prevent binge drinking and reduce the overall drinking population.
Photogravitational Axisymmetric Restricted Five-Body Problem Prachi Sachan, Rajiv Aggarwal, Amit Mittal Astronomy Reports, 2025 Abstract In the framework of photogravitational axisymmetric restricted five-body problem (PAR5BP), the existence and stability of the in-plane equilibrium points, the possible regions for motion are explored and analyzed numerically along with good agreement of the graphical results. We have determined the dynamics of the infinitesimal mass in the PAR5BP. We have determined the locations of the libration points (LPs) in the convex configuration. Further, the parametric evolution of the equilibrium points as the function of radiation parameter has been shown. The stability along with the zero velocity surface associated with the libration points are also investigated. It has been observed that none of the libration point is stable for any value of considered parameters.
A novel nonlinear SAZIQHR epidemic transmission model: mathematical modeling, simulation, and optimal control Abhishek Kumar, Tanvi, Rajiv Aggarwal Physica Scripta, 2025 This study presents a seven-compartmental nonlinear epidemic model to explore the dynamics and control of the epidemic. The model extends the traditional susceptible-infected-recovered (SIR) framework by including additional compartments for aware, infodemic, hospitalized, and quarantined populations. It also incorporates three Holling type II saturated nonlinear incidence rates to better represent the disease transmission process. The ‘infodemic population’ refers to those spreading misinformation about the disease, its spread, control, and treatment. The study examines disease dynamics in the absence of a vaccine and identifies two key equilibria: the disease-free equilibrium (DFE) and the endemic equilibrium (EE). It is found that the DFE is locally asymptotically stable when the basic reproduction number ( R 0 ) is below one and becomes unstable when R 0 exceeds one. The model’s behavior at R 0 = 1 is analyzed using center manifold theory, revealing a forward bifurcation. Additionally, the existence of a positive endemic equilibrium is confirmed for R 0 > 1 , with no backward bifurcation observed when R 0 ≤ 1 . The EE is also shown to be locally asymptotically stable when R 0 is greater than one. Furthermore, the study formulates and mathematically analyzes an optimal control problem. Finally, numerical simulations are presented to support the analytical results.
MODELING THE OPTIMAL INTERVENTIONS TO CURTAIL THE CLUSTER BASED COVID-19 PANDEMIC IN INDIA: EFFICACY OF PREVENTION MEASURES Applied and Computational Mathematics, 2021
Emerging therapeutic approaches to COVID-19 Indrakant K. Singh, Pratibha Kumari, Pooja Mittal, Amit Kumar, Bharti Singal, Gulam M. Hasan, Rajiv Aggarwal, Md. Amjad Kamal, Archana Singh, Md. Imtaiyaz Hassan Current Pharmaceutical Design, 2021
Existence and stability of equilibrium points in the problem of a geo-centric satellite including the earth’s equatorial ellipticity Nonlinear Dynamics and Systems Theory, 2019
Periodic orbits around L4 in the photogravitational restricted problem with oblate primaries International Conference on Applied and Computational Mathematics, 2011
RECENT SCHOLAR PUBLICATIONS
Analysis of Basins of Attraction in the Pseudo-Newtonian Photogravitational Restricted Four-Body Problem with Asteroid Belt Effects V Kumar, R Aggarwal, N Kumar Kinematics and Physics of Celestial Bodies 42 (2), 80-100 , 2026 2026
Mathematical model for Buruli ulcer and HIV co-infection with optimal control strategy R Kumar, R Aggarwal, Tanvi International Journal of Biomathematics, 2550167 , 2026 2026
Mathematical modeling of Buruli ulcer in fuzzy environment: global stability analysis R Kumar, R Aggarwal, Tanvi The European Physical Journal Plus 140 (11), 1101 , 2025 2025
Revealing the albedo’s impact on the dynamics of the perturbed restricted three-body problem S Chauhan, D Kumar, R Aggarwal, EI Abouelmagd, GA Elnashar Communications in Nonlinear Science and Numerical Simulation 150, 109048 , 2025 2025 Citations: 3
Dynamic analysis of Lyapunov and Halo orbits in the Proxima Centauri system OP Meena, M Lohani, H Mishra, R Aggarwal The European Physical Journal Plus 140 (10), 993 , 2025 2025 Citations: 1
Application of Fourier series to the dynamics of a test particle in the CR3BP with an oblate primary OP Meena, M Lohani, S Sen, D Mishra, R Aggarwal International Journal of Non-Linear Mechanics 172, 105030 , 2025 2025 Citations: 4
Comparison of Analytical and Numerical Methods to Solve Boundary‐Layer Natural Convection Problem for Various Prandtl Number Fluids D Kushawaha, S Yadav, R Aggarwal Heat Transfer 54 (3), 1807-1818 , 2025 2025
A fractional order age-structured model to study the effect of social awareness on alcohol consumption A Rajput, R Aggarwal Physica Scripta 100 (4), 045224 , 2025 2025 Citations: 1
Photogravitational Axisymmetric Restricted Five-Body Problem P Sachan, R Aggarwal, A Mittal Astronomy Reports 69 (1), 45-57 , 2025 2025
A novel nonlinear SAZIQHR epidemic transmission model: mathematical modeling, simulation, and optimal control A Kumar, Tanvi, R Aggarwal Physica Scripta 100 (1), 015002 , 2025 2025 Citations: 1
Fourier Series Methodology for Exploring the Periodic Orbits in the CR3BP with Spherical Primaries OP Meena, H Aggarwal, H Mishra, K Shaw, R Aggarwal Astronomy Reports 68 (12), 1317-1334 , 2024 2024 Citations: 1
Effect of the Pseudo Mean Motion on the Dynamics of Perturbed Elliptic Restricted Three-Body Problem B Kaur, SK Meena, RK Sharma, R Aggarwal Astronomy Reports 68 (9), 938-947 , 2024 2024
Study of stokes drag and radiation pressure in the restricted four-body problem with variable mass K Pal, A Mittal, R Aggarwal Astronomy Reports 68 (7), 698-727 , 2024 2024 Citations: 2
Unveiling the intricacies of attracting zones in magnetic binary systems: Investigating the impact of Yukawa correction V Kumar, R Aggarwal, SK Marig Astronomy and Computing 46, 100783 , 2024 2024 Citations: 2
The analysis of the photogravitational r4bp under the combined effect of stokes drag and oblateness with variable mass A Mittal, K Pal, R Aggarwal The Journal of the Astronautical Sciences 70 (6), 52 , 2023 2023 Citations: 4
Exploring the perturbed restricted three-body problem under the effect of Albedo and straight segment S Chauhan, R Aggarwal Astronomy Reports 67 (10), 1008-1018 , 2023 2023 Citations: 4
Effect of Stokes drag in the restricted four-body problem with variable mass A Mittal, K Pal, MS Suraj, R Aggarwal New Astronomy 103, 102042 , 2023 2023 Citations: 5
On the basins of convergence in the beyond-Newtonian spatial collinear circular restricted four-body problem with spinning primaries MS Suraj, FL Dubeibe, R Aggarwal, MC Asique, S Alhowaity, A Alhowaity New Astronomy 102, 102035 , 2023 2023 Citations: 4
Analysis of Resonant Curve in a Synchronous Satellite under the Gravitational Effect of the Sun, the Moon, and the Earth Including Its Oblateness using Poincare Section S Yadav, M Kumar, R Aggarwal Astronomy Reports 67 (6), 638-654 , 2023 2023
Fractional Order on Modeling the Transmission of Devastative COVID-19 Infection: Efficacy of Vaccination. A Rajput, R Aggarwal, A Sharma, SK Sahdev, M Kumar Applications & Applied Mathematics 18 (1) , 2023 2023
MOST CITED SCHOLAR PUBLICATIONS
A fractional order HIV-TB co-infection model in the presence of exogenous reinfection and recurrent TB Tanvi, R Aggarwal, YA Raj Nonlinear Dynamics, 1-25 , 2021 2021 Citations: 55
The analysis of restricted five–body problem within frame of variable mass MS Suraj, EI Abouelmagd, R Aggarwal, A Mittal New Astronomy 70, 12-21 , 2019 2019 Citations: 53
Stability of libration points in the restricted four-body problem with variable mass A Mittal, R Aggarwal, MS Suraj, VS Bisht Astrophysics and space science 361 (10), 329 , 2016 2016 Citations: 51
On the restricted four-body problem with the effect of small perturbations in the Coriolis and centrifugal forces MS Suraj, R Aggarwal, M Arora Astrophysics and Space Science , 2017 2017 Citations: 48
Dynamics of HIV-TB co-infection with detection as optimal intervention strategy Tanvi, R Aggarwal International Journal of Non-Linear Mechanics 120, 103388 , 2020 2020 Citations: 40
Stability analysis of a delayed HIV-TB co-infection model in resource limitation settings Tanvi, R Aggarwal Chaos, Solitons & Fractals 140 , 2020 2020 Citations: 37
Robe’s problem: its extension to 2+ 2 bodies B Kaur, R Aggarwal Astrophysics and Space Science 339 (2), 283-294 , 2012 2012 Citations: 37
Out-of-Plane Equilibrium Points and Regions of Motion in Photogravitational R3BP when the Primaries are Heterogeneous Spheroid with Three Layers MCA Md Sanam Suraj, Rajiv Aggarwal, Kumari Shalini New Astronomy , 2018 2018 Citations: 35
On the photo-gravitational restricted four-body problem with variable mass A Mittal, R Agarwal, MS Suraj, M Arora Astrophysics and Space Science 363 (5), 109 , 2018 2018 Citations: 34
A study of non-collinear libration points in restricted three body problem with stokes drag effect when smaller primary is an oblate spheroid M Jain, R Aggarwal Astrophysics and Space Science 358 (2), 51 , 2015 2015 Citations: 34
Optimal control strategies on COVID-19 infection to bolster the efficacy of vaccination in India A Rajput, M Sajid, Tanvi, C Shekhar, R Aggarwal Scientific Reports 11 (1), 1-18 , 2021 2021 Citations: 32
On the spatial collinear restricted four-body problem with non-spherical primaries MS Suraj, R Aggarwal, A Mittal, OP Meena, MC Asique Chaos, Solitons & Fractals 133, 109609 , 2020 2020 Citations: 30
Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential MS Suraj, EE Zotos, C Kaur, R Aggarwal, A Mittal International Journal of Non-Linear Mechanics 103, 113-127 , 2018 2018 Citations: 30
Exploring the fractal basins of convergence in the restricted four-body problem with oblateness MS Suraj, A Mittal, M Arora, R Aggarwal International Journal of Non-Linear Mechanics 102, 62-71 , 2018 2018 Citations: 29
Robe’s restricted problem of 2+ 2 bodies when the bigger primary is a Roche ellipsoid and the smaller primary is an oblate body B Kaur, R Aggarwal Astrophysics and space science 349 (1), 57-69 , 2014 2014 Citations: 29
On the fractal basins of convergence of the libration points in the axisymmetric five-body problem: the convex configuration MS Suraj, P Sachan, EE Zotos, A Mittal, R Aggarwal International Journal of Non-Linear Mechanics 109, 80-106 , 2019 2019 Citations: 27
Robe's restricted problem of 2+ 2 bodies when the bigger primary is a Roche ellipsoid B Kaur, R Aggarwal Acta Astronautica 89, 31-37 , 2013 2013 Citations: 27
On the Newton–Raphson basins of convergence associated with the libration points in the axisymmetric restricted five-body problem: The concave configuration MS Suraj, P Sachan, EE Zotos, A Mittal, R Aggarwal International Journal of Non-Linear Mechanics 112, 25-47 , 2019 2019 Citations: 26
On the modified circular restricted three-body problem with variable mass MS Suraj, R Aggarwal, MC Asique, A Mittal New Astronomy 84, 101510 , 2021 2021 Citations: 25
Assessing the effects of holling type-II treatment rate on HIV-TB co-infection R Aggarwal, T Kovacs Acta Biotheoretica 69 (1), 1-35 , 2021 2021 Citations: 25