Dr. Pawan Kumar Shaw

@bitmesra.ac.in

Assistant Professor, Department of Mathematics
Birla Institute of Technology Mesra

Dr. Pawan Kumar Shaw


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https://researchid.co/pawanshaw22
Dr. Pawan Kumar Shaw is an Assistant Professor in the Department of Mathematics with several years of experience in teaching and research in applied mathematics. He received his doctoral degree in Mathematics with a focus on fractional-order differential equations and nonlinear dynamical systems. His primary research interests include fractional calculus, stability and bifurcation analysis, mathematical epidemiology, ecological and population dynamics, and numerical methods for fractional differential equations.
Dr. Shaw’s research emphasizes the development and analysis of fractional-order mathematical models to better capture memory and hereditary effects in real-world systems. He has contributed to the qualitative analysis of nonlinear systems, including equilibrium analysis, basic reproduction numbers, and sensitivity analysis, as well as the design and implementation of efficient numerical schemes for fractional models. His work has been published in reputed journals.

EDUCATION

Ph.D. in Mathematics,
Department of Mathematics, National Institute of Technology (NIT) Jamshedpur, India, 2023

M.Sc. in Mathematics & Computing,
Department of Mathematics, Indian Institute of Technology (IIT) Guwahati, India, 2016

B.Sc. (Honours) in Mathematics,
Ramakrishna Mission Vivekananda Centenary College, Rahara, India, 2014

RESEARCH, TEACHING, or OTHER INTERESTS

Applied Mathematics, Modeling and Simulation, Numerical Analysis, Computational Mathematics
8

Scopus Publications

69

Scholar Citations

4

Scholar h-index

2

Scholar i10-index

Scopus Publications

  • Numerical investigation of pine wilt disease using fractal–fractional operator
    Anil Kumar, Pawan Kumar Shaw, Sunil Kumar
    Indian Journal of Physics, 2025
  • A fractional-order model for cattle–invertebrate competitive dynamics in a grassland setting
    Abhinav Tandon, Pawan Kumar Shaw
    Engineering Computations Swansea Wales, 2025
    Purpose The purpose of this study is to investigate the competitive dynamics between cattle and invertebrates for grass biomass in a grassland ecosystem using a fractional-order nonlinear mathematical model. Design/methodology/approach A fractional-order grassland competition model is formulated using the Caputo fractional derivative of order ρ ∈ (0, 1]. The qualitative behavior of the system is analyzed by establishing the non-negativity and boundedness of solutions, followed by a stability analysis of the equilibrium points. Numerical simulations are performed using a generalized fractional Runge–Kutta second-order (RK2) scheme to examine the influence of fractional orders and interspecific competition parameters on system dynamics. Findings The results demonstrate that the proposed model admits biologically feasible solutions that remain non-negative and bounded. Stability analysis reveals that fractional-order dynamics significantly affect the equilibrium behavior of the system. Numerical simulations show that varying the fractional order and competition coefficients leads to substantial changes in grass biomass and population dynamics. In particular, fractional-order models exhibit enhanced stability and reduced oscillatory behavior compared to classical integer-order models. Originality/value This study provides a novel fractional-order framework for modeling grassland competition involving cattle and invertebrates. The findings highlight the advantages of fractional-order models in capturing memory effects and improving stability characteristics, offering valuable insights for ecological modeling and sustainable grassland management.
  • A chaotic study of love dynamics with competition using fractal-fractional operator
    Anil Kumar, Pawan Kumar Shaw, Sunil Kumar
    Engineering Computations Swansea Wales, 2024
    PurposeThe objective of this work is to analyze the necessary conditions for chaotic behavior with fractional order and fractal dimension values of the fractal-fractional operator.Design/methodology/approachThe numerical technique based on the fractal-fractional derivative is implemented over the fractional model and analyzes the condition at the distinct values of fractional order and fractal dimension.FindingsThe obtained numerical solution from the numerical technique is analyzed at distinct fractional order and fractal dimension values, and it has been figured out that the behavior of the solution either chaotic or non-chaotic agrees with the condition.Originality/valueThe necessary condition is associated with the fractional order only. So, our work not only studies the condition with fractional order but also examines the model by simultaneously adjusting fractal dimension values. It is found that the model still has chaotic or non-chaotic behavior at certain fractal dimension values and fractional order values corresponding to the condition.
  • A numerical study on fractional differential equation with population growth model
    Sunil Kumar, Pawan Kumar Shaw, Abdel‐Haleem Abdel‐Aty, Emad E. Mahmoud
    Numerical Methods for Partial Differential Equations, 2024
    In this work, we developed two efficient and fast numerical technique to solve an initial value problem (IVP) of the linear and nonlinear fractional differential equations (FDEs) of orderα, 0 < α < 1. Here we have used the arbitrary order derivatives in Riemann style. The proposed algorithm are very accurate and provides the solutions directly without perturbations, linearization, or any other assumptions. Illustrating examples with numerical comparisons between the proposed algorithm and the exact and/or Euler method and the improved Euler method (IEM) are given to reveal the efficiency and the accuracy of our algorithm. These scheme has quadratic and cubic convergence rate which is faster than the Euler method and IEM for solving the IVP of FDEs. Moreover, we have discussed the behaviors through graphical representation of the obtained solutions. Furthermore, both methods will be useful for the treatment of disease models for further study.
  • Two New Quadratic Scheme for Fractional Differential Equation with World Population Growth Model
    Progress in Fractional Differentiation and Applications, 2023
  • Dynamical analysis of fractional plant disease model with curative and preventive treatments
    Pawan Kumar Shaw, Sunil Kumar, Shaher Momani, Samir Hadid
    Chaos Solitons and Fractals, 2022
  • A study of Ralston’s cubic convergence with the application of population growth model
    Sara S. Alzaid, Pawan Kumar Shaw, Sunil Kumar
    Aims Mathematics, 2022
    <abstract><p>This paper deals a new numerical scheme to solve fractional differential equation (FDE) involving Caputo fractional derivative (CFD) of variable order $ \\beta \\in ]0, 1] $. Based on a few examples and application models, the main objective is to show that FDE works more effectively than ordinary differential equations (ODEs). The proposed scheme is fractional Ralston's cubic method (RCM). The convergence analysis and stability analysis of the scheme is proved. The numerical scheme has been found without considering linearisation, perturbations, or any such assumptions. Finally, the efficiency of the proposed scheme will justify by solving a few examples of linear and non-linear FDEs with one application of FDE, world population growth (WPG) model of variable order $ \\beta \\in ]0, 1] $. Also, the comparison of fractional RCM scheme has been shown with the existing fractional Euler method (EM) and fractional improved Euler method (IEM).</p></abstract>
  • A numerical study of fractional population growth and nuclear decay model
    Sara S. Alzaid, Pawan Kumar Shaw, Sunil Kumar
    Aims Mathematics, 2022
    <abstract><p>This paper is devoted to solving the initial value problem (IVP) of the fractional differential equation (FDE) in Caputo sense for arbitrary order $ \\beta\\in(0, 1] $. Based on a few examples and application models, the main motivation is to show that FDE may model more effectively than the ordinary differential equation (ODE). Here, two cubic convergence numerical schemes are developed: the fractional third-order Runge-Kutta (RK3) scheme and fractional strong stability preserving third-order Runge-Kutta (SSRK3) scheme. The approximated solution is derived without taking any assumption of perturbations and linearization. The schemes are presented, and the convergence of the schemes is established. Also, a comparative study has been done of our proposed scheme with fractional Euler method (EM) and fractional improved Euler method (IEM), which has linear and quadratic convergence rates, respectively. Illustrative examples and application examples with the numerical comparison between the proposed scheme, the exact solution, EM, and IEM are given to reveal our scheme's accuracy and efficiency.</p></abstract>

RECENT SCHOLAR PUBLICATIONS

  • A fractional-order model for cattle–invertebrate competitive dynamics in a grassland setting
    A Tandon, PK Shaw
    Engineering Computations, 1-26 , 2026
    2026
  • AI-ENHANCED CUBIC CONVERGENCE RUNGE–KUTTA ALGORITHMS FOR SOLVING INITIAL VALUE PROBLEMS OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS
    PK Shaw, A Kumar, S Kumar
    IN Patent App. 202,531,102,599 , 2026
    2026
  • Numerical investigation of pine wilt disease using fractal–fractional operator: A Kumar et al.
    A Kumar, PK Shaw, S Kumar
    Indian Journal of Physics 99 (2), 367-393 , 2025
    2025
    Citations: 4
  • A chaotic study of love dynamics with competition using fractal-fractional operator
    A Kumar, PK Shaw, S Kumar
    Engineering Computations 41 (7), 1884-1907 , 2024
    2024
    Citations: 1
  • A numerical study on fractional differential equation with population growth model
    S Kumar, PK Shaw, AH Abdel‐Aty, EE Mahmoud
    Numerical Methods for Partial Differential Equations 40 (1), e22684 , 2024
    2024
    Citations: 29
  • Two New Quadratic Scheme for Fractional Differential Equation with World Population Growth Model
    PK Shaw, S Kumar, S Momani, S Hadid
    Progress in Fractional Differentiation and Applications 9 (4), 545-564 , 2023
    2023
    Citations: 2
  • Dynamical analysis of fractional plant disease model with curative and preventive treatments
    PK Shaw, S Kumar, S Momani, S Hadid
    Chaos, Solitons & Fractals 164, 112705 , 2022
    2022
    Citations: 21
  • A study of Ralston's cubic convergence with the application of population growth model
    SS Alzaid, PK Shaw, S Kumar
    AIMS Mathematics 7 (6), 11320-11344 , 2022
    2022
    Citations: 6
  • A numerical study of fractional population growth and nuclear decay model
    SS Alzaid, PK Shaw, S Kumar
    AIMS Mathematics 7 (6), 11417-11442 , 2022
    2022
    Citations: 6

MOST CITED SCHOLAR PUBLICATIONS

  • A numerical study on fractional differential equation with population growth model
    S Kumar, PK Shaw, AH Abdel‐Aty, EE Mahmoud
    Numerical Methods for Partial Differential Equations 40 (1), e22684 , 2024
    2024
    Citations: 29
  • Dynamical analysis of fractional plant disease model with curative and preventive treatments
    PK Shaw, S Kumar, S Momani, S Hadid
    Chaos, Solitons & Fractals 164, 112705 , 2022
    2022
    Citations: 21
  • A study of Ralston's cubic convergence with the application of population growth model
    SS Alzaid, PK Shaw, S Kumar
    AIMS Mathematics 7 (6), 11320-11344 , 2022
    2022
    Citations: 6
  • A numerical study of fractional population growth and nuclear decay model
    SS Alzaid, PK Shaw, S Kumar
    AIMS Mathematics 7 (6), 11417-11442 , 2022
    2022
    Citations: 6
  • Numerical investigation of pine wilt disease using fractal–fractional operator: A Kumar et al.
    A Kumar, PK Shaw, S Kumar
    Indian Journal of Physics 99 (2), 367-393 , 2025
    2025
    Citations: 4
  • Two New Quadratic Scheme for Fractional Differential Equation with World Population Growth Model
    PK Shaw, S Kumar, S Momani, S Hadid
    Progress in Fractional Differentiation and Applications 9 (4), 545-564 , 2023
    2023
    Citations: 2
  • A chaotic study of love dynamics with competition using fractal-fractional operator
    A Kumar, PK Shaw, S Kumar
    Engineering Computations 41 (7), 1884-1907 , 2024
    2024
    Citations: 1
  • A fractional-order model for cattle–invertebrate competitive dynamics in a grassland setting
    A Tandon, PK Shaw
    Engineering Computations, 1-26 , 2026
    2026
  • AI-ENHANCED CUBIC CONVERGENCE RUNGE–KUTTA ALGORITHMS FOR SOLVING INITIAL VALUE PROBLEMS OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS
    PK Shaw, A Kumar, S Kumar
    IN Patent App. 202,531,102,599 , 2026
    2026