Dr. Md. Nur Alam


Associate Professor, Faculty of Science, Department of Mathematics
Pabna University of Science and Technology



Dr. Md Nur Alam was born in Panchagarh, Bangladesh on 01 March 1986. He completed his B. Sc. (Hons.) and M. Sc. (Thesis) in Mathematics from Rajshahi University, Rajshahi, Bangladesh, in 2008 and 2009, respectively. He was also awarded M. Phil Degree in Mathematics in the field of mathematical physics in 2015 from PUST. He successfully completed his Ph. D. in Computational Mathematics from the University of Science and Technology of China (USTC, China) under a very prestigious CAS-TWAS Scholarship. His Ph. D. thesis was mainly concerned with CAGD and Computer Graphics. In 2012, he joined in a Lecture of Mathematics, PUST. In 2014, he joined as an Assistant Professor of Mathematics, PUST. From 2020 to date, He is doing as an Associate Professor of Mathematics, PUST. His current research interests include fluid mechanics, computer graphics, CAGD, IGA, mathematical physics, integral and fractional order of PDEs. He has published more than 80 papers.


Ph.D. in Computational Mathematics, Department of Mathematics, University of Science and Technology of China (USTC), China, 2020, (2016-2020). Thesis title: Non-Uniform Subdivision Surfaces via Eigen Polyhedron, Supervisor: Professor Dr. Xin Li


Computational mathematics; mathematical physics; nonlinear dynamics; Fractional Calculus; nonlinear Integral and Fractional PDEs; Computational Fluid Dynamics (CFD); Computer Graphics; Computer Aided Geometric Design


Scopus Publications

Scopus Publications

  • The New Soliton Configurations of the 3D Fractional Model in Arising Shallow Water Waves
    Md. Nur Alam, Imran Talib, and Cemil Tunç

    Springer Science and Business Media LLC

    Md. Sabur Uddin

    Journal of Mechanics of Continua and Mathematical Sciences
    In this analysis, we apply prominent mathematical systems like the modified (G’/G)-expansion method and the variation of (G’/G)-expansion method to the nonlinear fractional-order biological population model. We formulate twenty-three mathematical solutions, which are clarified hyperbolic, trigonometric, and rational. Using MATLAB software, we illustrate two-dimensional, three-dimensional, and contour shapes of our obtained solutions. These mathematical systems depict and display its considerate and understandable technique that generates a king type shape, singular king shapes, soliton solutions, singular lump and multiple lump shapes, periodic lump and rouge, the intersection of king and lump wave profile, and the intersection of lump and rogue wave profile. Measuring our return and that gained in the past released research shows the novelty of our analysis. These systems are also capable to represents various solutions for other fractional models in the field of applied mathematics, physics, and engineering.

    Md. Nur Alam

    Journal of Mechanics of Continua and Mathematical Sciences
    The existing article examines the mathematical model (MM) representing electrical engineering (EE). We implement the unified technique (UT) to discover new wave solutions (WS) and to erect numerous kinds of solitary wave phenomena (SWP) for the studied model (SM). The SM is one of the models that have vital applications in the area of EE. The taken features provide a firm mathematical framework and may be necessary to the WSs. As an outcome, we get new kinds of WSs from. With 3-d, density, contour, and 2-d for different values of time parameters, mathematical effects explicitly manifest the suggested algorithm’s full reliability and large display. We implement a few figures in 3-d, density, contour, and 2-d for diverse values of time parameters to express that these answers have the properties of soliton waves.

  • Inclined magnetic field and variable viscosity effects on bioconvection of Casson nanofluid slip flow over non linearly stretching sheet
    Noman Sarwar, Muhammad Imran Asjad, Sajjad Hussain, Md. Nur Alam, and Mustafa Inc

    Elsevier BV

  • Some new results of nonlinear model arising in incompressible visco-elastic Kelvin–Voigt fluid
    Md. Nur Alam, Shariful Islam, Onur Alp İlhan, and Hasan Bulut


  • New Results of Some of the Conformable Models Arising in Dynamical Systems
    Md Nur Alam, Onur Alp Ilhan, Jalil Manafian, Muhammad Imran Asjad, Hadi Rezazadeh, and Haci Mehmet Baskonus

    Hindawi Limited
    This article investigates the new results of three nonlinear conformable models (NLCMs). To study such varieties of new soliton structures, we perform the generalized Kudryashov (GK) method. The obtained new results are defined in the styles of the exponential and rational functions. The derived new soliton structures are stable, serviceable, and fitting to embrace the conformable dynamics, chaotic vibrations, global bifurcations, optimal control problems, fluid mechanics, plasma physics, system identification, local bifurcations, control theory and resonances, and so many. The outcomes declare that the process is hugely valuable and accessible for investigating nonlinear conformable order models treated in theoretical physics.

  • The Effects of Magneto-Radiative Parameters on the Heat Transfer Mechanism in H<inf>2</inf>O Composed by Cu-Al<inf>2</inf>O<inf>3</inf>Hybrid Nanomaterial: Numerical Investigation
    Wahid Khan, Umar Khan, Adnan, Basharat Ullah, Naveed Ahmed, Ilyas Khan, Aisha M. Alqahtani, and Md. Nur Alam

    Hindawi Limited
    The analysis of thermal performance in second generation of nanofluids (hybrid nanofluids) attained much attention of the researchers, scientists, engineers, and industrialists. These fluids have ultra-high thermal characteristics due to which their broad applications could be found in many areas of technological world. Therefore, a novel analysis regarding the heat transfer is conducted over a stretched surface by considering combined convection, thermal radiations, and magnetic field. The hybrid nanofluid is synthesized by Cu-Al2O3 guest hybrid-nanomaterial and host liquid H2O. The hybrid flow model is solved numerically and decorated the results over the region of interest. It is drawn that the velocity drops by increasing the strength of Cu-Al2O3 fraction and applied Lorentz forces. Furthermore, the thermal performance of Cu-Al2O3/H2O augmented against stronger thermal radiations, volumetric fraction, and magnetic field effects.

  • On Sum Degree-Based Topological Indices of Some Connected Graphs
    Muhammad Tanveer Hussain, Navid Iqbal, Usman Babar, Tabasam Rashid, and Md Nur Alam

    Hindawi Limited
    In mathematical chemistry, molecular structure of any chemical substance can be expressed by a numeric number or polynomial or sequence of number which represents the whole graph is called topological index. An important branch of graph theory is the chemical graph theory. As a consequence of their worldwide uses, chemical networks have inspired researchers since their development. Determination of the expressions for topological indices of different derived graphs of graphs is a new and interesting problem in graph theory. In this article, some graphs which are derived from honeycomb structure are studied and obtained their exact results for sum degree-based indices. Additionally, a comparison is shown graphically among all the indices.

  • Entropy Generation Analysis for MHD Flow of Hybrid Nanofluids over a Curved Stretching Surface with Shape Effects
    Basharat Ullah, Umar Khan, Hafiz Abdul Wahab, Ilyas Khan, and Md. Nur Alam

    Hindawi Limited
    The characteristic of magnetohydrodynamic flow of viscous fluids is explained here. The energy equation behavior is studied in the presence of heat, viscous dissipation, and joule heating. The major emphasis of this study is the physical behavior of the entropy optimization rate. Based on the implementation of curvilinear coordinates, the basic flow equations are established. Nonlinear partial differential expressions are reduced by appropriate transformation to the ordinary differential system. In the engineering and industrial processes, nanoparticles and their shape have practical consequences. For this reason, we give a detailed investigation of the shape impacts on the flow through the curved stretching surface of nanoparticles. The flow equations are reduced into a number of nonlinear differential equations which are solved numerically using a useful numerical approach called Runge-Kutta-4 (RK-4). The shooting method is first used to reduce the equations to a number of problems of first order, and then the RK-4 approach is used for solution. Impacts for entropy optimization, Bejan number, velocity, concentration, and temperature of several physical parameters are graphically studied.

  • Computing Fault-Tolerant Metric Dimension of Connected Graphs
    Uzma Ahmad, Sara Ahmed, Muhammad Javaid, and Md Nur Alam

    Hindawi Limited
    For a connected graph, the concept of metric dimension contributes an important role in computer networking and in the formation of chemical structures. Among the various types of the metric dimensions, the fault-tolerant metric dimension has attained much more attention by the researchers in the last decade. In this study, the mixed fault-tolerant dimension of rooted product of a graph with path graph with reference to a pendant vertex of path graph is determined. In general, the necessary and sufficient conditions for graphs of order at least 3 having mixed fault-tolerant generators are established. Moreover, the mixed fault-tolerant metric generator is determined for graphs having shortest cycle length at least 4.

  • Studies of Metal Organic Networks via M-Polynomial-Based Topological Indices
    Muhammad Tanveer Hussain, Muhammad Javaid, Sajida Parveen, Hafiz Muhammad Awais, and Md Nur Alam

    Hindawi Limited
    Topological index (TI) is a graph-theoretic tool that is used to study different physical and structural properties of the networks in various disciplines of science such as computer science, chemistry, and information technology. In this article, we study transition metal tetra-cyano-benzene organic networks by computing their M-polynomials and various topological indices (TIs). At the end, a comparison is also included between all the computed degree-based topological indices to show their betterness.

  • An Efficient Analytical Approach for the Periodicity of Nano/Microelectromechanical Systems' Oscillators
    Naveed Anjum, Jamshaid Ul Rahman, Ji-Huan He, Md. Nur Alam, and Muhammad Suleman

    Hindawi Limited
    Periodic behavior analysis of nano/microelectromechanical systems (N/MEMS) is an essential field owing to their many promising applications in microinstruments. The interesting and unique properties of these systems, particularly, small size, batch fabrication, low power consumption, and high reliability, have fascinated researchers and industries to implement these structures for the production of different microdevices. The dynamic oscillatory behavior of N/MEMS is very intricate due to the various types of nonlinearities present in these structures. The foremost objective of this study is to explore the periodicity of oscillatory problems from N/MEMS. The variational iteration method (VIM), which has been considered as an effective approach for nonlinear oscillators, is coupled with the Laplace transform to obtain the approximate analytic solution of these nonlinear vibratory systems with fewer computations. This coupling of VIM and Laplace transform not only helps in the identification of the Lagrange multiplier without getting into the details of the cryptic theory of variations, but also finds the frequency-amplitude relationship and the analytic approximate solution of N/MEMS. A generalized vibratory equation for N/MEMS is followed by three examples as special cases of this generalized equation are given to elucidate the effectivity of the coupling. The solution obtained from the Laplace-based VIM not only exhibits good agreement with observations numerically but also higher accuracy yields when compared to other established techniques in the open literature.

  • Regarding on the Results for the Fractional Clannish Random Walker's Parabolic Equation and the Nonlinear Fractional Cahn-Allen Equation
    Md. Nur Alam, Onur Alp İlhan, Md. Sabur Uddin, and Md. Abdur Rahim

    Hindawi Limited
    In this research, the Ψ , Φ -expansion scheme has been implemented for the exact solutions of the fractional Clannish Random Walker’s parabolic (FCRWP) equation and the nonlinear fractional Cahn-Allen (NFCA) equation. Some new solutions of the FCRWP equation and the NFCA equation have been obtained by using this method. The diverse variety of exact outcomes such as intersection between rough wave and kinky soliton wave profiles, intersection between lump wave and kinky soliton wave profiles, soliton wave profiles, kink wave profiles, intersection between lump wave and periodic wave profiles, intersection between rough wave and periodic wave profiles, periodic wave profiles, and kink wave profiles are taken. Comparing our developed answers and that got in previously written research papers presents the novelty of our investigation. The above techniques could also be employed to get exact solutions for other fractional nonlinear models in physics, applied mathematics, and engineering.

  • General Solution for Unsteady MHD Natural Convection Flow with Arbitrary Motion of the Infinite Vertical Plate Embedded in Porous Medium
    Sami Ul Haq, Hammad Khaliq, Saeed Ullah Jan, Aisha M. Alqahtani, Ilyas Khan, and Md. Nur Alam

    Hindawi Limited
    This article has concentrated on heat transfer analysis in the unsteady MHD natural convection flow of viscous fluid under radiation and uniform heat flux over an infinite vertical plate embedded in a porous medium. Overall solutions are found for temperature as well as velocity by the Laplace transform techniques. In the literature, the solutions that have been achieved are rare, meet with all the initial and boundary conditions imposed, and can make general solutions for any problem with motion with this form’s methodological relevance. Also, few different cases of engineering applications are discussed. Solutions are plotted graphically through the use of the Mathcad software to analyze how the variation is taking place in the physical behavior of the viscous fluid flow with respect to the change in a distinct physical parameter.

  • Triple Solutions with Stability Analysis of MHD Mixed Convection Flow of Micropolar Nanofluid with Radiation Effect
    Hazoor Bux Lanjwani, Muhammad Saleem Chandio, M. Imran Anwar, Amnah S. Al-Johani, Ilyas Khan, and Md. Nur Alam

    Hindawi Limited
    This paper deals with two-dimensional steady boundary layer flow, heat, and mass transfer characteristics of micropolar nanofluid past on exponentially stretching/shrinking surface. The effect of different physical parameters like magnetic field, buoyancy, thermal radiation, and connective heat transfer are examined. Furthermore, similarity solutions are obtained by similarity transformation on the governing system of partial differential equations. The shooting method with help of the Maple software is used to achieve the numerical solutions of the equations. For the different ranges of the applied parameters, triple solutions are obtained for both cases of the surface. In view of the triple solutions, stability analysis is performed by bvp4c in the MATLAB software, where only first solution is found feasible which is discussed. The main findings of the first solution indicate the skin friction, drag force, heat, and mass transfer rates are increasing for the λ &gt; 0 and decreasing for λ &lt; 0 as the K is enhanced. The velocity profiles decrease with increase in magnetic, slip velocity, and suction parameters. The temperature profiles increase with increase in magnetic, thermophoresis, thermal radiation, and Brownian motion parameters, whereas concentration profiles reduce with increase in Schmitt number and Brownian motion.

  • On Vertex Degree-Based Topological Indices for Fixed Branching Vertices of Trees
    Muzamil Hanif, Akhlaq Ahmad Bhatti, Muhammad Javaid, and Md Nur Alam

    Hindawi Limited
    The Gourava indices and hyper-Gourava indices are graph invariants, related to the degree of vertices of a graph G . Let T n , b denote the collection of all chemical trees with n vertices where b denotes the number of branching vertices, 1 ≤ b &lt; n − 2 / 2 . In the current paper, maximum value for the abovementioned topological indices for different classes 1 T n , b and 2 T n , b of T n , b is determined and the corresponding extremal trees are characterized.

  • On the Studies of Dendrimers via Connection-Based Molecular Descriptors
    Aqsa Sattar, Muhammad Javaid, and Md Nur Alam

    Hindawi Limited
    Topological indices (TIs) have been utilized widely to characterize and model the chemical structures of various molecular compounds such as dendrimers, neural networks, and nanotubes. Dendrimers are extraordinarily comprehensible, globular, artificially synthesized polymers with a structure of frequently branched units. A mathematical approach to characterize the molecular structures by manipulating the topological techniques, including numerical graphs invariants is the present-day line of research in chemistry. Among all the defined descriptors, the connection-based Zagreb indices are considered to be more effective than the other classical indices. In this manuscript, we find the general results to compute the Zagreb connection indices (ZCIs), namely, first ZCI (1st ZCI), second ZCI (2nd ZCI), modified 1st ZCI, modified 2nd ZCI, and modified 3rd ZCI. Furthermore, we compute the multiplicative ZCI (MZCI), namely, first MZCI (1st MZCI), second MZCI (2nd MZCI), third MZCI (3rd MZCI), fourth MZCI (4th MZCI), modified 1st MZCI, modified 2nd MZCI, and modified 3rd MZCI. In addition, we compare the calculated values with each other in order to check the superiority.

  • Reliable analysis for the drinfeld-sokolov-wilson equation in mathematical physics

  • New results of the time-space fractional derivatives of kortewege-de vries equations via novel analytic method
    Mariam Sultana, Uroosa Arshad, Md. Nur Alam, Omar Bazighifan, Sameh Askar, and Jan Awrejcewicz

    Symmetry performs an essential function in finding the correct techniques for solutions to time space fractional differential equations (TSFDEs). In this article, we present the Novel Analytic Method (NAM) for approximate solutions of the linear and non-linear KdV equation for TSFDs. To enunciate the non-integer derivative for the aforementioned equation, the Caputo operator is manipulated. Furthermore, the formula implemented is a numerical way that is postulated from Taylor’s series, which confirms an analytical answer in the form of a convergent series. For delineation of the efficiency and functionality of the method in question, four applications are exemplified along with graphical interpretation and numerical solutions to finitely illustrate the behavior of the solution to this equation. Moreover, the 3D graphs of some of these numerical examples are plotted with specific values. Observing the effectiveness of this process, we can easily decide that this process can be implemented to other TSFDEs applied in the mathematical modeling of a real-world aspect.

  • Heatline visualization of MHD natural convection heat transfer of nanofluid in a prismatic enclosure
    Tarikul Islam, Md. Nur Alam, Muhammad Imran Asjad, Nazma Parveen, and Yu-Ming Chu

    Springer Science and Business Media LLC
    AbstractTemperature transfer by virtue of natural convection for visualizing heat transport characteristics through heatline method within a prismatic cavity filled with Cu-H2O nanofluid considering two different temperature boundary conditions is performed numerically. Two top inclined walls are warmed-up at low temperature whilst the bottom wall is heated two different heated conditions such as uniform temperature condition and linear temperature condition. Two vertical walls are insulated. Finite element technique of Galerkin weighted residual form is employed for solving nonlinear partial differential equations for numerical calculation. Heatlines, isotherm contours, streamline contours, and Nusselt number are employed for displaying numerical simulated results for the model parameters entitled nanoparticles volume fraction, Hartmann number and Rayleigh number. The outcomes indicate that heat transfer rate has a significant impact on thermal boundary condition and shape of the nanoparticles. The temperature transfer value enhances significantly for higher Rayleigh number as well as nanoparticles volume fraction. Hartmann number has a positive impact on fluid flow and temperature transport. The characteristics of heat transport using heatlines method are also performed for predicting the better energy transform compared to isotherm contours. In addition, different types of nanofluids are also employed to examine the best heat transport performance.

  • The unified technique for the nonlinear time-fractional model with the beta-derivative
    Hijaz Ahmad, Md. Nur Alam, Md. Abdur Rahim, Maged F Alotaibi, and Mohamed Omri

    Elsevier BV

  • Impact of undulation on magneto-free convective heat transport in an enclosure having vertical wavy sides
    Md. Fayz-Al-Asad, Md. Nur Alam, A.M. Rashad, and Md. Manirul Alam Sarker

    Elsevier BV

  • New computational results for a prototype of an excitable system
    Hijaz Ahmad, Md. Nur Alam, and Mohamed Omri

    Elsevier BV