Research Guidance

Ph.D. Scholars

  • Aijaz Ahmad Mir, JRF-CSIR (Awarded): Mathematical estimation of thermal stress on human body (September 2015).
  • Aijaz Ahmad Najar, JRF-CSIR (Awarded): Variational finite element approach to study heat and oxygen transfer in human body(March 2016).
  • Aasma Rafiq, DST-INSPIRE Fellow (Awarded): Mathematical and Numerical Investigation of heat and drug diffusion in human subjects at extreme environmental conditions (December, 2016).
  • Khalid Nazir, UGC Project Fellow (Awarded), Mathematical Analysis of the heat and mass transfer in biological tissue with special reference to tumors (February 2018) (Co-Supervisor: Prof. B. A. Ganie, CORD, UoK).
  • Saqib Mubarak, SET (Awarded): Mathematical and Numerical study of drug and tracer diffusion in biological tissues (August 4, 2021). [Notification]
  • Ahsan ul Haq Lone, NET (Awarded): Mathematical modeling of transport and exchange of oxygen and carbon-dioxide in human body (October 12, 2021). [Notification]
  • Faizan Ahmad Zargar, (Awarded): Mathematical modelling of kinetics of malignant tumors in Kashmir region (Co-Supervisor: Dr. Mudasir Ashraf, Physics, AMU). (October 30, 2023) [Notification]
  • Roohi Jan (Awarded): Mathematical Analysis of Enzyme-Substrate complex and its binding properties (Co-Supervisor: Dr. Fouzia Rasheed, Clinical Biochemistry, UoK). [March 31, 2023] (Notification)
  • Nayied Naveed, NET, (under supervision), A Wavelet-based Numerical Study of Epidemic Models (Co-Supervisor: Dr. Firdous Ahmad Shah, South Campus, UoK).
  • Ms. Sumaira Anjum, (Completed course work in May 2024), Co-Supervisor: Dr. Tanveer Ali Dar, Department of Clinical Biochemistry, University of Kashmir, Srinagar.
  • Ms. Sabira Ali, (Completed course work in May 2024), Co-Supervisor: Dr. Aijaz Ahmad Mir, Govt. Women's College, Anantnag.
  • Ms. Ulfat Bashir, (Joined in May 2024) (Co-Supervisor: Dr. Firdous A Shah, South Campus, Anantnag)

M. Phil. Scholars

  • Aasma Rafiq (Awarded: August 2013); Modeling thermoregulation in human eye at extreme climatic conditions.
  • Khalid Nazir (Awarded: April 2015); Mathematical and Numerical study of hyperthermia and cancerous tumors.

Research Projects (Project Fellows/Junior Research Fellows):

  • JK DST Major Research Project: Mathematical and numerical investigation of cooperativity of enzymes and glucose synthesis in biological tissues (Sanctioned in January 2024).
  • DST-SERB Major Research Project-2018 (Rs 15,57,600): Modeling hypothermia and hypoxia associated problems to the people living at high altitudes of Himalayan regions (2018-2021).
  • NBHM sponsored Major Research Project- 2016 (Rs 14,18,100): Mathematical Analysis on the Drug Diffusion and Absorption Rate in Biological Tissues; with special reference to the Transdermal Drug Delivery System. (2016-2019).
  • UGC Major Research Project- March, 2013 (Rs 9,25,400) Mathematical study of cold stress and related problems in human beings of J & K during winter (Khalid Nazir) - 2013-2016(completed).
  • DST-SERB Major Research Project- September, 2013 (Rs 12,24,000), Mathematical and Numerical analysis for thermal stress on human peripherals in our state (Fida Hussain) -2013-2016 (completed)
  • Project Mentor of the Minor Research Project entitled “Mathematical study of calcium distribution in oocytes” sponsored by MP Council of Science and Technology, Bhopal (Parvaiz Ah. Naik) - (completed).
  • Project Mentor of the Minor Research Project entitled “ Special functions and their properties” sponsored by MP Council of Science and Technology, Bhopal, (Farooq Ah. Sheikh) - (completed).      

Publications (Selected Research Papers):

  • Roohi Jan and M. A. Khanday (2023), A mathematical analysis of cooperativity and fractional saturation of oxygen in hemoglobin, Commun.Fac.Sci.Univ.Ank.Ser. A1 Math. Stat. Volume 72, Number 1, Pages 118–128 (2023) DOI:10.31801/cfsuasmas.1029614
ISSN 1303-5991 E-ISSN 2618-6470

  • Saqib Mubarak and M.A. Khanday (2022), A mathematical model to study thermoregulation and heat-transfer processes in hypothermic neonates under varibale physiological parameters, Journal of "Computer Methods in Biomechanics and Biomedical Engineering", Taylor and Franscis, DOI: 10.1080/10255842.2022.2117550  (Accepted in September, 2022)

  • Roohi Jan and Khanday MA (2022), An algebraic mathematical model for non-competitive enzyme inhibitors with slow and fast subsystems, Applied Mathematics E-Notes, Vol. 22 (2022), 362- 370, ISSN: 1607-2510,  http://www.math.nthu.edu.tw/∼amen/

  • Khanday MA and Saqib Mubarak (2022), Mathematical modeling of concentration/ timeactivity profiles of radiotracers in positron emission tomography, Computer Methods in Biomechanics and Biomedical Engineering, Imaging & Visualization, Taylor and Francis, https://doi.org/10.1080/21681163.2022.2064333. (April 2022). 

  • Ahsan ul Haq Lone and Khanday MA, (2022), Mathematical analysis of oxygen and carbon dioxide exchange in the human capillary and tissue system, Computer Methods in Biomechanics and Biomedical Engineering, Taylor and Francis, https://doi.org/10.1080/10255842.2022.2053115 (March 2022).

  • Ahsan ul Haq Lone, MA Khanday, Saqib Mubarak and FA Reshi (2022), Heat distribution and the condition of hypothermia in the multi-layered human head: A mathematical model, Computer Methods in Biomechanics and Biomedical Engineering, Taylor and Francis, https://doi.org/10.1080/10255842.2022.2047953.

  • Saqib Mubarak and M.A. Khanday (2021), Mathematical modeling of drug-diffusion from multi-layered capsules/tablets and other drug-delivery devices, Journal of "Computer Methods in Biomechanics and Biomedical Engineering", Taylor and Franscis, https://doi.org/10.1080/10255842.2021.1985477.

  • Khanday M.A. and Roohi Jan (2021), Transformation of Glucokinase under Variable Rate Constants and Thermal Conditions: A Mathematical Model,   Applications and Applied Mathematics: An International Journal (AAM), Vol. 16(2), 953-964. : https://digitalcommons.pvamu.edu/aam/vol16/iss2/10.

  • Ahsan ul Haq Lone, Khanday M.A. and Saqib Mubarak. (2021), A four-compartment model to estimate oxygen and carbon dioxide exchange concentrations via blood using eigenvalue approach” South East Asian Journal of Mathematics and Mathematical Sciences, vol.17(2), 367-384, ISSN:2582-0850.

  • Saqib Mubarak and Khanday M.A. (2022), A mathematical model on the dynamics of radioactive tracer flow in PET scan, Applied Mathematics E-Notes, 22(2022), 383-392, https://www.emis.de/journals/AMEN/

  • Khanday M.A. et al. (2021), An analytical approach to study the drug diffusion through transdermal drug delivery system, Applied Mathematics E-Notes, ISSN 1607-2510, ESCI, Vol. 21(August-2021), 198-208, ISSN: 1607-2510.

  • Saqib Mubarak, M.A. Khanday and Ahsan ul Haq Lone (2020), Variational finite element approach to study heat transfer in the biological tissue of premature infants, Journal of Thermal Biology, Elsevier, Vol. 92(August 2020), (IF 2.361).

  • Khalid Nazir, Khanday M.A. and Ganai B.A. (2017), 2D model on heat regulation in human body with dermal tumor, Proceeding Electronic Journal of Differential Equations, Texas State University, San Marcos USA, 24(2017), 75-83.

  • Khanday M.A. (2016), A review paper entitled “ Modeling heat and oxygen regulation in human body: An overview”, GAMS Journal of Mathematics and Biosciences, A Special Issue of 2016.

  • Aasma Rafiq and Khanday M. A. (2016), Thermal behavior of human eye in relation with change in blood perfusion, porosity, evaporation and ambient temperature. Journal of Thermal Biology, Elsevier, online July 21, 2016.

  • Khanday M. A.  and Fida Hussain (2016), Thermal Stability of Biological Tissues and their Behaviour in Cold Conditions: A Mathematical Model, International Journal of Biomathematics, DOI: 10.1142/S1793524516500662, online 22 March, 2016.

  • Khanday M.A., Aasma Rafiq and Khalid Nazir (2016), Mathematical models for drug diffusion through the compartments of blood and tissue medium, Alexandria Journal of Medicine, Elsevier, online July, 2016.

  • Mir Aijaz and Khanday M.A. (2016), Studying the effects of the heat stress on the various layers of human skin using damage function, International Jour. of Comp. Mat. Sci. and Engineering, Imperial College, London Press, Vol 5(1), 2016, DOI: 10.1142/S2047684116500032, 1650003 (12 pages), online March 25, 2016.

  • Khanday M.A., and Khalid Nazir (2016), Eigenvalue Expansion Approach to Study Bio-Heat Equation, Journal of Multiscale Modeling, Vol. 7(2), 1650002 (8 pages), World Scientific Publishing Company DOI: 10.1142/S1756973716500025.

  • Khanday M.A. et al. (2015), Finite Element Approach to Study the Behavior of Fluid Distribution in the Dermal Regions of Human Body due to Thermal Stress, Journal of Egyptian Mathematical Society, Elsevier, vol 23(3), 568-573, online February 23, 2015. doi:10.1016/j.joems.2014.12.009

  • Khanday M.A. and Aijaz Najar (2015), Maclaurin's Series Approach for the Analytical Solution of Oxygen Transport to the Biological Tissues Through Capillary Bed, Journal of Medical Imaging and Health Informatics, Vol. 5(5), 959-963, September, 2015, DOI: http://dx.doi.org/10.1166/jmihi.2015.1487.

  • Khanday M. A., Fida Hussain and Khalid Nazir (2015), Tissue necrosis and passage of fluid due to cold stress from the thermally damaged human body peripherals: A mathematical model, International Journal of Computational Materials Science and Engineering, World Scientific Publishing Company, Available online, June 18, 2015, Vol. 4(2), 1550012 (14 pages), Imperial College London Press, DOI: 10.1142/S2047684115500128

  • Khanday M. A. and Khalid Nazir (2015), Temperature distribution in biological tissues under the influence of external heat source, Bull. of Cal. Math. Soc. 107(2), 145-152.

  • Khanday M.A. and Fida Hussain (2015), Crank-Nicholson Scheme for the Estimation of Thermal Disturbance on the Peripheral Tissues of Human Body Subjected to Oscillatory Boundary Condition and Time Dependent Heat Source, Journal of Multiscale Modeling, Vol. 6, No. 1 1550001 (10 pages), Imperial College London Press, DOI: 10.1142/S1756973715500018.

  • Mir Aijaz and Khanday M.A. (2015), Temperature distribution and thermal damage of peripheral tissue in human limbs during the heat stress: A Mathematical Model, Journal of Mechanics in Medicine and Biology, World Scientific Publishing Company, Singapore online from November 30, 2015.

  • Khanday, M.A. (2014), Numerical study of partial differential equations to estimate thermoregulation in human dermal regions for temperature dependent thermal conductivity, Egyptian Journal of Mathematics, Elsevier, Vol.  22(1), 152-155.  (Available online, July 17, 2013), ISSN 1110-256X.

  • Khanday, M.A., Mir Aijaz and Aasma Rafiq (2014), Numerical estimation of the fluid distribution pattern in human dermal regions with heterogeneous metabolic fluid generation, Journal of Mechanics in Medicine and Biology, World Scientific, Vol. 15(1), Available online from August 22, 2014, doi/abs/10.1142/S0219519415500013.

  • Mir Aijaz, M.A. Khanday and Aasma Rafiq (2014), Variational Finite Element Approach to Study the Thermal Stress in Multi-layered Human Head, International Journal of Biomathematics, World Scientific Company, Vol. 7(6), 1450073, available online from October 2, 2014.

  • Khanday M.A. and Aijaz Najar (2014), Variational finite element approach to estimate the behavior of oxygen diffusion in the biological tissue via plasma and capillary layers, International Journal of Modern Mathematical Sciences, Vol. 12(1), 1-9, ISSN: 2166-286X

  • Khanday, M. A. and Aasma Rafiq (2014), Variational finite element method to study the absorption rate of drug at various compartments through transdermal drug delivery system, Alexandria Journal of Medicine, Elsevier, Vol. 51(3). 219-223, (online Available from November 22, 2014).

  • Khanday M.A. and Aijaz Najar (2014), Mathematical model for the transport of oxygen in the living tissue through capillary bed, Journal of Mechanics in Medicine and Biology, World Scientific Publishing Company, Available online from December 23, 2014. doi/abs/10.1142/S0219519415500554.

  • Khanday M. A. et al. (2014), Variational finite element approach to estimate the heat distribution in multi-layered human eye, Bul. Cal. Math. Soc. 106(2), 93-104.

  • Khanday M.A. and Fida Hussain (2014), Explicit formula of finite difference method to estimate human peripheral tissue temperatures during exposure to severe cold stress, Journal of Thermal Biology, Elsevier,Vol. 48(February, 2015), 51-55, Available online from December 24, 2014.

  • Khanday, M.A., Mir Aijaz and Aasma Rafiq (2013), Mathematical analysis on the treatment of cancerous tumors based on local hyperthermia, Journal of energy, heat and mass transfer, Vol. 35(2), ISSN 0970-9991.

  • Khanday M. A., et al. (2012), Modeling Effect of slaughtering on the conservation and migration of animal species, International Journal of Mathematical Archive, Vol. 13(2), 466-470, ISSN No. 2229-5046.

  • Khanday M. A., et al. (2012), Theoretical analysis on the stability and persistence of interacting species during dispersion, Research Journal of Pure Algebra, Vol. 12(2), 71-76. ISSN No. 2248-9037.

  • Khanday, M. A. and Saxena, V. P. (2009), Finite element approach for the study of thermoregulation in human head exposed to cold environment. Proceedings Journal of American Institute of Physics, Vol. 1146, 375-385. ISSN NO. 0094-243x.

  • Khanday, M. A. and Saxena, V. P. (2009), Mathematical estimation of cold effect in human dermal regions. International Journal of Applied Mathematics and Computation, Vol. 11 (1): 17-29. ISSN NO. 0974-4665(P) 0974-4673 (E).

  • Khanday, M. A. (2009), Theoretical Study of Response on Human Thermoregulation due to Sweat Evaporation, GAMS, Journal of Mathematics and Mathematical Bio-Sciences, Taylor and Francis, vol. 32, 76-83, ISSN NO. 0974-2689.

  • Khanday, M. A. and Saxena, V. P. (2009), Finite element estimation of one dimensional unsteady state heat regulation in human head exposed to cold environment, Journal of Biological Systems, World Scientific, Vol. 17(4): 853-863. ISSN NO. 0218-3390 (Print) 1793-6470 (Electronic).

  • Khanday, M. A. and Saxena, V. P. (2009), Mathematical estimation of human physiological disturbances in human dermal parts at extreme conditions: A one dimensional steady state case, Journal of Analysis in Theory and Applications, Springer, Vol. 25(4): 325-332. ISSN NO. 1672-4070(Print) 1573-8175.

Books/Scripts

  • Introduction to Modeling and Biomathematics (2015), Ariana Book Publishers, New Delhi. ISBN 978-93-85497-25-4(HB), ISBN 978-93-85497-26-1(PB), Pp (248).

  • Theory of Ordinary Differential Equations-I (2006), Published by Directorate of Distance Education, University of Kashmir, Srinagar, ISBN: 978-93-82097-14-3.

  • Complex Analysis-I (2009), Published by Directorate of Distance Education, University of Kashmir, Srinagar, ISBN: 978-93-82097-14-3.

  • Lebesgue Integration Theory (2010), Published by Directorate of Distance Education, University of Kashmir, Srinagar, ISBN: 978-93-82097-14-3.

  • Introduction to Mathematical Modeling (2011), Published by Directorate of Distance Education, University of Kashmir, Srinagar, ISBN: 978-93-82097-14-3.

  • Canonical Forms in Linear Algebra (2011), Published by Directorate of Distance Education, University of Kashmir, Srinagar (in press), ISBN: 978-93-82097-14-3.

  • Mathematical Biology (2011), Published by Directorate of Distance Education, University of Kashmir, Srinagar, ISBN: 978-93-82097-14-3.