| Research Group Title |
Numerical and Analytical Solution of ODEs and PDEs |
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| Area of Research |
Numerical and analytical solution techniques for the problems of Fluid Dynamics, Fractional Calculus, Fuzzy Conditions, Heat and Mass Transfer, and Epidemiology |
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| Theme of Research / Goals |
Fluid Dynamics, MHD, Nanofluid, Fractional Calculus, Heat and Mass Transfer, Epidemiology |
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| Faculty Members |
Dr. Muhammad Imran Asjad, Dr. Muhammad Aziz ur Rehman, Dr. Akhtar Hussain, Dr. Javaria Akram, Dr. Sidra Afzal |
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| Collaborating UMT Departments |
Mathematics |
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| Collaborating National Institutes |
• Dr. Muhammad Imran, GCU Faisalabad
• Prof. Dr. Mudassar Nazar, BZU Multan
• Dr. Nazia Shahmir, Bahria University, Islamabad
• Dr. Iffat Zehra, Air University, Islamabad
• Dr. Mubashir Qayyum, FAST-NUCES, Lahore
• Dr. Syed Tauseef Saeed, UOL, Lahore |
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| Collaborating International Institutes |
• Prof. Dr. Dumitru Baleanu, Cankaya University, Turkey
• Prof. Dr. Abdon Atangana, University of Free State, South Africa
• Prof. Dr. Noreen Sher Akbar, Prince Mohammad Bin Fahd University, Saudi Arabia
• Prof. Dr. Muhammad Ramzan, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
• Prof. Dr. Saraswati Acharya, Kathmandu University, Nepal
• Gilbert Chambashi, Unicaf University, Lusaka, Zambia |
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| Names of Active Senior Students |
• Arfan Ali
• Madsar Kaleem |
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| Short Description of the Research Theme |
The group focuses on developing and applying both numerical and analytical solution techniques for ordinary and partial differential equations arising in diverse scientific and engineering contexts. Emphasis is placed on problems in fluid dynamics, heat and mass transfer, fractional calculus, fuzzy systems, and epidemiology, where modeling complexity often prevents closed-form solutions. Using methods such as finite difference, finite element, Runge–Kutta, homotopy analysis, and fractional-order operators, the group formulates efficient and accurate solution strategies. The research also explores hybrid approaches combining analytical insights with computational algorithms to tackle nonlinearity, uncertainty, and multi-scale effects. Through this integrated approach, the group aims to provide robust, versatile frameworks for analyzing and predicting system behavior, contributing to both theoretical advancements and practical problem-solving in science, engineering, and public health. |
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| SDGs Covered |
SDG3, SDG4, SDG9 |
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| List of 5 relevant publications: |
- Majid, S.Z., Asjad, M.I., Kumar, S. et al. Dynamical Study with Exact Travelling Waves with High Amplitude Solitons to Clannish Random Walker’s Parabolic Equation. Qual. Theory Dyn. Syst. 24, 14 (2025). https://doi.org/10.1007/s12346-024-01175-w
- J. Akram, I. Zehra, Numerical simulation of bioconvective peristaltic flow of saline-based hybrid nanofluid with second-order slip velocities through an endoscope under electroosmotic effects, International Journal of Modern Physics B, (2025), DOI:10.1142/S0217979225502674.
- S. Afzal, E. Ahmad, M. Qayyum et al., Fractional modeling and analysis of heat and mass transfer in nanofluid via He–Laplace framework, AIP Advances, (2025).
- Tariq MM, Riaz MB, Ur Rehman MA, Dilawaiz. Unraveling the complexity of solitary waves in the Klein-Fock-Gordon equation: dynamical insights into bifurcation and chaos analysis. Model Earth Syst Environ. 2025;11(1):51. doi:10.1007/s40808-024-02249-z.
- Hussain A, Ibrahim TF, Birkea FM Osman, Yahya MS, Hassaballa AA, Mukalazi H. Abundant different types of soliton solutions for fractional modified KdV equation using auxiliary equation method. Sci Rep. 2025;15:43518. doi:10.1038/s41598-025-26779-3.
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