Professor of Mathematics
Dhirubhai Ambani University
Research Interests
Neural Networks
Fractional Calculus
Numerical Analysis
Mathematical Modelling
Teaching Interests
Soft Computing, Nonlinear Dynamics, Differential Equations, Calculus, Real & Complex Analysis
Publications
Selected Publications: 10 (Citations: 3200+, h-index: 32). A total of 100+ papers can be accessed in his researcher index, such as Google Scholar.
Pushpendra Kumar, Vedat Suat Erturk, Marina Murillo-Arcila, and V. Govindaraj. “A new form of L1-Predictor-Corrector scheme to solve multiple delay-type fractional order systems with the example of a neural network model.” Fractals 31, no. 4 (2023): 2340043. https://doi.org/10.1142/S0218348X23400431
Pushpendra Kumar, Tae H. Lee, and Vedat Suat Erturk. “A fractional-order multi-delayed bicyclic crossed neural network: Stability, bifurcation, and numerical solution.” Neural Networks (2025): 107436. https://doi.org/10.1016/j.neunet.2025.107436
Pushpendra Kumar, Tae H. Lee, and Vedat Suat Erturk. “A novel fractional-order neutral-type two-delayed neural network: Stability, bifurcation, and numerical solution.” Mathematics and Computers in Simulation 232 (2025): 245-260. https://doi.org/10.1016/j.matcom.2025.01.001
Pushpendra Kumar, Tae H. Lee, and Vedat Suat Erturk. “A novel two-delayed tri-neuron neural network with an incomplete connection.” Nonlinear Dynamics 112 (2024): 20269-20293. https://doi.org/10.1007/s11071-024-10066-3
Pushpendra Kumar, Tae H. Lee, and Vedat Suat Erturk. “A novel fractional-order cascade tri-neuron Hopfield neural network: stability, bifurcations, and chaos.” Qualitative Theory of Dynamical Systems 23 (2024): 236. https://doi.org/10.1007/s12346-024-01096-8
Pushpendra Kumar, V. Govindaraj, and Vedat Suat Erturk. “A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population.” Chaos, Solitons & Fractals 161 (2022): 112370. https://doi.org/10.1016/j.chaos.2022.112370
Pushpendra Kumar, Vedat Suat Erturk, Marina Murillo-Arcila, and Charis Harley. “Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid.” International Journal of Nonlinear Sciences and Numerical Simulation 24, no. 6 (2022): 2089-2111. https://doi.org/10.1515/ijnsns-2021-0278
Pushpendra Kumar. “A nonlinear mathematical model to describe the transmission dynamics of the citrus canker epidemic.” An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 0 (2025): 1-13. https://doi.org/10.36922/ijocta.1507
Pushpendra Kumar. “A new fractional-order model for defining the dynamics of ending student strikes at a university.” Boletín de la Sociedad Matemática Mexicana 30, no. 3 (2024): 91. https://doi.org/10.1007/s40590-024-00667-8
Pushpendra Kumar, and Vedat Suat Erturk. “A fractional-order improved FitzHugh-Nagumo neuron model.” Chinese Physics B 34 (2025): 018704. https://doi.org/10.1088/1674-1056/ad8a46
Dr. Pushpendra Kumar is a dedicated researcher and academic specializing in neural networks, fractional calculus, mathematical modeling, and numerical analysis. He has worked as a postdoctoral researcher at Jeonbuk National University, South Korea. He has also served as a visiting professor at Istanbul Okan University, Turkey; as a research associate at Near East University, Cyprus; and as a research professor at the University of Johannesburg, South Africa, reflecting his global academic footprint. Recognized among the “World’s Top 2% Scientists” by Elsevier and Stanford University in 2023, 2024, and 2025, Dr. Kumar has also been a recipient of the prestigious IMU Breakout Graduate Fellowship from the International Mathematical Union (Germany) and London Mathematical Society. He has published more than 100 research papers in reputed international journals and has edited a book entitled “Recent Developments in Fractional Calculus: Theory, Applications, and Numerical Simulations.”