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

  • Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach
    Ahmed Refaie Ali, Md. Nur Alam, and Mst. Wahida Parven

    Springer Science and Business Media LLC
    AbstractThe space–time fractional Fokas–Lenells (STFFL) equation serves as a fundamental mathematical model employed in telecommunications and transmission technology, elucidating the intricate dynamics of nonlinear pulse propagation in optical fibers. This study employs the Sardar sub-equation (SSE) approach within the STFFL equation framework to explore uncharted territories, uncovering a myriad of optical soliton solutions (OSSs) and conducting a thorough analysis of their bifurcations. The discovered OSSs encompass a diverse array, including bright-dark, periodic, multiple bright-dark solitons, and various other types, forming a captivating spectrum. These solutions reveal an intricate interplay among bright-dark solitons, complex periodic sequences, rhythmic breathers, coexistence of multiple bright-dark solitons, alongside intriguing phenomena like kinks, anti-kinks, and dark-bell solitons. This exploration, built upon meticulous literature review, unveils previously undiscovered wave patterns within the dynamic framework of the STFFL equation, significantly expanding the theoretical understanding and paving the way for innovative applications. Utilizing 2D, contour, and 3D diagrams, we illustrate the influence of fractional and temporal parameters on these solutions. Furthermore, comprehensive 2D, 3D, contour, and bifurcation analysis diagrams scrutinize the nonlinear effects inherent in the STFFL equation. Employing a Hamiltonian function (HF) enables detailed phase-plane dynamics analysis, complemented by simulations conducted using Python and MAPLE software. The practical implications of the discovered OSS solutions extend to real-world physical events, underlining the efficacy and applicability of the SSE scheme in solving time–space nonlinear fractional differential equations (TSNLFDEs). Hence, it is crucial to acknowledge the SSE technique as a direct, efficient, and reliable numerical tool, illuminating precise outcomes in nonlinear comparisons.

  • Applications of nonlinear longitudinal wave equation with periodic optical solitons wave structure in magneto electro elastic circular rod
    Mujahid Iqbal, Md. Nur Alam, Dianchen Lu, Aly R. Seadawy, Nahaa E. Alsubaie, and Salisu Ibrahim

    Springer Science and Business Media LLC

  • Modulation instability and comparative observation of the effect of fractional parameters on new optical soliton solutions of the paraxial wave model
    Md. Mamunur Roshid, Md. Nur Alam, Onur Alp İlhan, Md. Abdur Rahim, Md. Mehedi Hassen Tuhin, and M. M. Rahman

    Springer Science and Business Media LLC
    AbstractThis work focuses on the study of the paraxial wave model with a space–time fractional form. This model has more importance for describing light propagation in nonlinear optical fibers and telecommunication lines. The main aim of this work is to observe the effect of the fractional parameters and compare the truncated $$M$$ M -fraction with the beta-fraction, conformable fraction form, and classical form of the PW model. For this observation, we applied the Simplest equation technique to acquire analytical solutions to the space–time (spatiotemporal) $$M$$ M -fractional paraxial wave model. We are able to acquire several new optical soliton solutions, including periodic waves, kink-type waves, rogue-type waves, and several novel periodic waves, by providing the appropriate fractional parametric values. These solutions have significance for shedding light on a number of physical phenomena in the realms of optical fiber and communication sciences. The diverse values of fractional parameters and the three-dimensional and contour plot graphs of certain chosen solutions are depicted, which are the most accurate physical characterizations of the outcomes. We also sketch the comparative graph of diverse fractional forms and the classical form of the paraxial wave equation in two-dimensional plots. Consequently, our findings represent an important breakthrough in this complex area and help further develop our comprehension of the behavior of solitons.

  • The application of cosine similarity measures with Laplacian energy to q-rung orthopair fuzzy graphs in decision-making problems
    Mohamed Atheeque A., Sharief Basha S., Nune Pratyusha, C. Raghavendra Reddy, Md Nur Alam, Hijaz Ahmad, Nainaru Tarakaramu, and Sreenivasulu K.

    AIP Publishing
    Q-rung orthopair fuzzy sets (q-ROFS), which are better than the intuitionistic and Pythagorean fuzzy sets, are a significant tool for expressing ambiguous information. Their key feature is that their ability to represent a larger space of uncertain information is based on the fact that the product of the qth power of the membership degree and the qth power of the degrees of non-membership is equal to or less than 1. Under these circumstances, we train group decision-making problems in the study using q-rung orthopair fuzzy inclination associations. Through the calculation of the standard deviation of one separable q-rung orthopair inclination association to the others and the unclear evidence of q-rung orthopair fuzzy inclination connections, we propose a novel approach to estimate the qualified reputation weights of authority. The “internal” and “impartial” evidence of authority is taken into consideration by this new mindset. Subsequently, we included the weights of authorities into the q-rung orthopair fuzzy inclination relations and used a relative similarity approach to determine the relevance of replacements and the best substitutes. The planned techniques' usefulness and realism are demonstrated by the contrast analysis with additional methods through mathematical demonstrations, both of which show the fuzzy set’s membership degree and non-membership degree, respectively.

  • Bifurcation, phase plane analysis and exact soliton solutions in the nonlinear Schrodinger equation with Atangana's conformable derivative
    Md. Nur Alam, Mujahid Iqbal, Mohammad Hassan, Md. Fayz-Al-Asad, Muhammad Sajjad Hossain, and Cemil Tunç

    Elsevier BV

  • Bifurcation analysis and new exact complex solutions for the nonlinear Schrödinger equations with cubic nonlinearity
    Md Nur Alam, Onur Alp İlhan, Hemel Sharker Akash, and Imran Talib

    Springer Science and Business Media LLC

  • Design of dual loop controller for boost converter based on PI controller
    Kifayat Ullah, Muhammad Ishaq, Muhammad Ajmal Naz, Mostafizur Rahaman, Arsalan Muhammad Soomar, Hijaz Ahmad, and Md. Nur Alam

    AIP Publishing
    Boost converters are widely used in industry for many applications, such as electrical vehicles, wind energy systems, and photovoltaic energy systems, to step up the low voltages. Using the topology structure of the DC–DC boost circuit, this paper studied and designed a dual loop control method based on proportional integral controllers for improving the converter efficiency. The inner loop and outer loop controls of the traditional boost circuit are adopted in MATLAB/Simulink software to make the output of the system more stable. The input voltage is set to 24 V DC, and the desired output voltage varies from 36 to 48 V. Through simulation verification, the influence of a 1 kW sudden load connection by using a switch at a nominal output voltage of 48 V DC is studied, and the results show that it reduces the transient output voltage dips during the sudden load connection. Simulation analysis verifies the design scheme of the system, reduces the fluctuation in output voltage and power, reduces the output current ripple, minimizes the dip in voltage to a minimum possible value, and improves the dynamic characteristics and overall efficiency of the converter.

  • An Enhanced Hybrid Model Based on CNN and BiLSTM for Identifying Individuals via Handwriting Analysis
    Md. Abdur Rahim, Fahmid Al Farid, Abu Saleh Musa Miah, Arpa Kar Puza, Md. Nur Alam, Md. Najmul Hossain, Sarina Mansor, and Hezerul Abdul Karim

    Tech Science Press

  • Unified existence results for nonlinear fractional boundary value problems
    Imran Talib, Asmat Batool, Muhammad Bilal Riaz, and Md. Nur Alam

    American Institute of Mathematical Sciences (AIMS)
    <abstract><p>In this work, we focus on investigating the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. By extending the framework of the technique based on well-ordered coupled lower and upper solutions, we guarantee the existence of solutions in a sector defined by these solutions. One notable aspect of our study is that the proposed approach unifies the existence results for the problems that have previously been discussed separately in the literature. To substantiate these findings, we have added three illustrative examples.</p></abstract>

  • Heat generation/absorption effect on natural convective heat transfer in a wavy triangular cavity filled with nanofluid
    Tarikul Islam, Md. Nur Alam, Shafiullah Niazai, Ilyas Khan, Md. Fayz-Al-Asad, and Sultan Alqahtani

    Springer Science and Business Media LLC
    AbstractThis study is numerically executed to investigate the influence of heat generation or absorption on free convective flow and temperature transport within a wavy triangular enclosure filled by the nanofluid taking the Brownian effect of nanoparticles. The water (H2O) is employed as base fluid and copper (Cu) as nanoparticles for making effective Cu–H2O nanofluids. The perpendicular sinusoidally wavy wall is cooled at low temperature while the horizontal bottom sidewall is heated non-uniformly (sinusoidal). The inclined wall of the enclosure is insulated. The governing dimensionless non-linear PDEs are executed numerically with the help of the Galerkin weighted residual type finite element technique. The numerically simulated results are displayed through average Nusselt number, isothermal contours, and streamlines for the various model parameters such as Hartmann number, Rayleigh number, heat generation or absorption parameter, nanoparticles volume fraction, and undulation parameter. The outcomes illustrate that the temperature transport rate augments significantly for the enhancement of Rayleigh number as well as nanoparticles volume fraction whereas reduces for the increment of Hartman number. The heat transfer is significantly influenced by the size, shape, and Brownian motion of the nanoparticles. The rate of heat transport increases by 20.43% considering the Brownian effect for 1% nanoparticle volume. The thermal performance increases by 8.66% for the blade shape instead of the spherical shape of nanoparticles. In addition, heat transfer is impacted by the small size of nanoparticles. The thermal transport rate increases by 35.87% when the size of the nanoparticles reduces from 100 to 10 nm. Moreover, the rate of heat transmission increases efficiently as the undulation parameter rises. It is also seen that a crucial factor in the flow of nanofluids and heat transmission is the heat generation/absorption parameter that influences temperature distribution, heat transfer rates, and overall thermal performance.

  • Bifurcation Analysis and Solitary Wave Analysis of the Nonlinear Fractional Soliton Neuron Model
    Md. Nur Alam, Hemel Sharker Akash, Uzzal Saha, Md. Shahid Hasan, Mst. Wahida Parvin, and Cemil Tunç

    Springer Science and Business Media LLC

  • Influence of magnetic field on MHD mixed convection in lid-driven cavity with heated wavy bottom surface
    Mst. Umme Mahmuda Maya, Md. Nur Alam, and Ahmed Refaie Ali

    Springer Science and Business Media LLC
    AbstractThis study investigates the influence of a rectangular heat source on magnetohydrodynamic hybrid convection flow in a lid-driven cavity. The effects of various parameters, such as the heat source size, magnetic field strength, and heat absorption/generation, are analyzed. The results show that increasing the heat source size decreases the average Nusselt number along the heated wall. The average Nusselt number also decreases with higher magnetic field strength and heat generation, while it increases with heat absorption. The major finding is to apply an important technique the Galerkin weighted residual technique of the finite element (FE) method to solve the non-dimensional equations and the associated boundary conditions. The isotherms are used to show the temperature distribution in a domain. Streamline present the flow field in the enclosure. However, it is easy to realize the direction and intensity of the heat transfer particularly in convection problems which the path of heat flux is perpendicular and the isotherm due to convection effect. Thus, the purpose of this research is to study the results of mixed convection. The effects of location and height of the partitions are considered for the various Richardson numbers. Fluid flow field, thermal field and heat transfer are presented through the streamlines and isotherms, respectively. Results are substantiated relating to the published work.

  • 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.