International Journals

1. Numerical simulation of the time fractional Gray-Scott model on 2D space domains using radial basis function, Journal of Mathematical Chemistry, 62 (2024), pp 836-864 https://doi.org/10.1007/s10910-023-01571-8 Published: 27 January 2024 (with Harshad Sakariya)

2. Thermal damage analysis in tissue caused by electromagnetic radiation using space–time collocation method, Journal of Thermal Biology, 117 (2023) 103715, Published online on 15 September 2023. DOI: https://doi.org/10.1016/j.jtherbio.2023.103715 (With Bhagya Shree Meena)

3. Chebyshev spectral method for the variable-order fractional mobile–immobile advection–dispersion equation arising from solute transport in heterogeneous media. Journal of Engineering Mathematics 142, 1 (2023). https://doi.org/10.1007/s10665-023-10288-1 (With Rupali Gupta)

4. Computational study on 2D three-phase lag bioheat model during cryosurgery using RBF meshfree method. Journal of Thermal Biology,  114 (2023) 103575 DOI: https://doi.org/10.1016/j.jtherbio.2023.103575. (With Rohit Verma)

5. Temperature response in skin tissue during hyperthermia based on three-phase-lag bioheat model using RBF meshfree method, Numerical Heat Transfer, Part A: Applications, 2023 (Published online: 24 Feb 2023) https://doi.org/10.1080/10407782.2023.2182386  (With Bhagya Shree Meena)

6. Space-time pseudospectral method for the variable-order space-time fractional diffusion equation, Mathematical Sciences (2023) (Published online: 21 Feb 2023 ) https://doi.org/10.1007/s40096-023-00510-7 (With Rupali Gupta) 

7. Computational study on 2D space-time fractional single-phase-lag bioheat model using RBF and Chebyshev polynomial based space-time collocation method.  Waves in Random and Complex Media (Published Online : 19 October 2022).  https://doi.org/10.1080/17455030.2022.2136418  (With Bhagya Shree Meena)

8. Numerical study on heat distribution in biological tissues based on three-phase lag bioheat model. Palestine Journal of Mathematics 11 (Special Issue III) (2022), 1-11 (With Rohit Verma) 

9. Solution of fractional order SIR epidemic model using residual power series method . Palestine Journal of Mathematics 11 (Special Issue III) (2022), 12-24 (With Rakesh Meena)

10. Numerical simulation of variable-order fractional differential equation of nonlinear Lane-Emden type appearing in astrophysics. International Journal of Nonlinear Sciences and Numerical Simulation (Published online: 28 April 2022) https://doi.org/10.1515/ijnsns-2021-0092 (with  Rupali Gupta)

11. Numerical Solution of Space-Time Fractional Klein-Gordon Equation by Radial Basis Functions and Chebyshev Polynomials. International Journal of Applied and Computational Mathematics  7, 201 (2021). https://doi.org/10.1007/s40819-021-01139-7 (with Hitesh Bansu)

12. Computational Study on Skin Tissue Freezing Using Three-Phase Lag Bioheat Model." ASME  Journal of Heat Transfer. November 2021; 143(11): 111201. DOI: https://doi.org/10.1115/1.4051764  (with Rohit Verma)

13. Analysis of fractional-order population model of diabetes and effect of remission through lifestyle intervention,  International Journal of Applied and Computational Mathematics 7(2):53 (2021), https://doi.org/10.1007/s40819-021-01001-w  (with Rupali Gupta)

14. The Chebyshev collocation method for a class of time fractional convection‐diffusion equation with variable coefficients, Mathematical Methods in the Applied Sciences, 44(8) pp 6666-6678, 2021, DOI: https://doi.org/10.1002/mma.7215 (with Vijay Saw)

15. Collocation method for time fractional diffusion equation based on the Chebyshev polynomials of second kind, International Journal of Applied and Computational Mathematics 6(4): 117 (2020). DOI: https://doi.org/10.1007/s40819-020-00878-3 (with Vijay Saw)

16. Computational study on constant and sinusoidal heating of skin tissue using radial basis functions, Computers in Biology and Medicine, Vol 121, (2020), DOI:https://doi.org/10.1016/j.compbiomed.2020.103808 (with Rohit Verma)

17. Numerical solution of space-time fractional PDEs using RBF-QR and Chebyshev polynomials, Applied Numerical Mathematics Vol 143, (2019) DOI: https://doi.org/10.1016/j.apnum.2019.04.012, (with Cecile Piret).

18. Numerical solution of fraction Bagley–Torvik boundary value problem based on Chebyshev collocation method, International Journal of Applied and Computational Mathematics, 5(3):68 (2019) https://doi.org/10.1007/s40819-019-0653-8. (with Vijay Saw)

19. Numerical solution of space and time fractional telegraph equation: a meshless approach, International Journal of Nonlinear Sciences and Numerical Simulation, Volume 20, Issue 3-4, Pages 325–337 ,  (2019),  DOI: https://doi.org/10.1515/ijnsns-2018-0087  (with Hitesh Bansu) 

20. Second kind Chebyshev polynomials for solving space fractional advection - dispersion equation using collocation method, Iranian Journal of Science and Technology, Transactions A: Science, 43:1027-1037, 2019  https://doi.org/10.1007/s40995-018-0480-5 (with Vijay Saw) 

21. Numerical study on thermal therapy of triple layer skin tissue using  fractional bioheat model, International Journal of Biomathematics, Vol. 11, No. 4 (2018) 1850052 (24 pages)  https://doi.org/10.1142/S1793524518500523 (with R. S. Damor and A. K. Shukla)

22. Fourth kind shifted Chebyshev polynomials for solving space fractional order advection dispersion equation based on collocation method and finite difference approximation, International Journal of Applied and Computational Mathematics, Vol 4:82 (2018). https://doi.org/10.1007/s40819-018-0517-7 (with Vijay Saw) 

23. Dual phase lag bio-heat transfer during cryosurgery of lung cancer: comparison of three heat transfer models, Journal of Thermal Biology, Volume 69, October 2017, pp 228-–237. https://doi.org/10.1016/j.jtherbio.2017.08.005 (with Ajay Kumar, Prof. V. K. Katiyar and Shirley Telles)

24. Phase change heat transfer during cryosurgery of lung cancer using hyperbolic heat conduction model, Computer in Biology and Medicine, Volume 84, 1 May 2017, pp 20-29 https://doi.org/10.1016/j.compbiomed.2017.03.009 (with Ajay Kumar, Prof. V. K. Katiyar and Shirley Telles)

25. Fuzzy similarity measure based spectral clustering framework for noisy image segmentation, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 25, No. 4 (2017) 649–673. https://doi.org/10.1142/S0218488517500283 (with Subhanshu Goyal, M. A. Zaveri, A. K. Shukla) 

26. Solution of fractional bioheat equation in terms of Fox’s H-function, Springer Plus (2016) 5:111. https://doi.org/10.1186/s40064-016-1743-2 (with R. S. Damor, and A. K. Shukla)

27. Numerical analysis of triple layer skin tissue freezing using non-Fourier heat conduction, Journal of Mechanics in Medicine and Biology, Volume 16, Issue 02, March 2016. https://doi.org/10.1142/S0219519416500172 (with Sonalika Singh)

28. Freezing of Biological Tissues during Cryosurgery Using Hyperbolic Heat Conduction Model, Mathematical Modelling and Analysis, Vol 20 (4), pp 443-456. https://doi.org/10.3846/13926292.2015.1064486 (with Sonalika Singh)

29. A Survey on Graph partitioning approach to spectral clustering, Journal of Computer Science & Cybernetics, Vol 20, Issue 4, (2015), pp 443-456 DOI: https://doi.org/10.15625/1813-9663/31/1/4108 (Subhanshu Goyal, M. A. Zaveri, A. K. Shukla)

30. Numerical study on triple layer Skin Tissue Freezing using dual phase lag bio heat model, International Journal of Thermal Science, Vol 86, 2014, pp 12-20. https://doi.org/10.1016/j.ijthermalsci.2014.06.027 (with Sonalika Singh)

31. A study on the effect of metabolic heat generation on biological tissue freezing, The Scientific World Journal, Article ID 398386, 2013, 7 pages. http://dx.doi.org/10.1155/2013/398386 (with Sonalika Singh)

32. Numerical simulation of fractional bio heat equation in hyperthermia treatment, Journal of Mechanics in Medicine and Biology, Vol 14 (2014), https://doi.org/10.1142/S0219519414500183 . (with Ramesh S Damor and A K Shukla)

33. Numerical solution of fractional diffusion equation model for freezing in finite media, International Journal of Engineering Mathematics,  2013 (Article ID 785609), 8 pages. http://dx.doi.org/10.1155/2013/785609 (with Ramesh S Damor and A K Shukla)

34. Numerical solution of fractional bioheat equation with constant and sinusoidal heat flux condition on skin tissue, American Journal of Mathematical Analysis,  Vol 1, No. 2 (2013): 20-24. DOI: 10.12691/ajma-1-2-1  (with Ramesh S Damor and A K Shukla)

35. Mathematical modeling of freezing and thawing process in tissues: a porous media approach, International Journal of Applied Mechanics, vol. 2, no. 3 (2010) pp617–633. https://doi.org/10.1142/S1758825110000688  (with V. K. Katiyar)

36. Numerical modeling of pulsatile flow of blood through a stenosed tapered artery under periodic body acceleration, Journal of Mechanics in Medicine and Biology, Vol. 10, No. 2 (2010) 251–272. https://doi.org/10.1142/S0219519410003393  (with G. Varshney and V. K. Katiyar)

37. Effect of magnetic field on the blood flow in artery having multiple stenosis:a numerical study, International Journal of Engineering, Science and Technology, Vol. 2, No. 2 (2010), pp. 67-82 (with Prof. V. K. Katiyar and Gaurav Varshney )

38. Mathematical Modeling of Pulsatile Blood Flow and Heat Transfer Characteristics in Stenosed Artery, International Journal of Fluid Mechanics Research, Vol. 37, No. 4, (2010) pp305-324.  https://doi.org/10.1615/InterJFluidMechRes.v37.i4.20  (with G. Varshney and V. K. Katiyar)

39. Transient analysis on alloy freezing in finite media with energy generation and convective cooling, International Journal of Applied Mechanics and Engineering, Vol 15, No. 4 (2010) pp1155-1168 (with V. K. Katiyar) 

International Proceedings

1. Kumar S., Bansu H. (2020) Meshless method for the numerical solution of space and time fractional wave equation, In:  Harizanov S., Lazarov R. and Margenov S.(Eds), International Workshop on Numerical Solution of Fractional Differential Equations and Applications (NSFDE&A'20), SOZOPOL, Bulgaria. 

2. Damor R.S., Kumar S., Shukla A.K. (2014) Temperature Distribution in Living Tissue with Fractional Bioheat Model in Thermal Therapy. In: Patel H., Deheri G., Patel H., Mehta S. (eds) Proceedings of International Conference on Advances in Tribology and Engineering Systems. Lecture Notes in Mechanical Engineering. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1656-8_44  

3. Kumar S., Katiyar V. K. (2006) Numerical simulation of thawing process of biological tissues as porous media during cryosurgery, presented in 5th world congress on Biomechanics, Munich (Germany) from July, 29    to Aug 4, 2006. Abstract in: Journal of Biomechanics Vol-39 Supp 1, pp S384  DOI:https://doi.org/10.1016/S0021-9290(06)84549-5.

Book Chapters 

1. Meena, B.S., Kumar, S. (2023). Temperature Distribution During Hyperthermia Using a 2D Space-Time Fractional Bioheat Model in Irregular Domain. In: Giri, D., Gollmann, D., Ponnusamy, S., Kouichi, S., Stanimirović, P.S., Sahoo, J.K. (eds) Proceedings of the Ninth International Conference on Mathematics and Computing. ICMC 2023 2023. Lecture Notes in Networks and Systems, vol 697. Springer, Singapore. https://doi.org/10.1007/978-981-99-3080-7_18  

2. Meena, R.K., Kumar, S. (2023). A Study on Fractional SIS Epidemic Model Using RPS Method. In: Giri, D., Gollmann, D., Ponnusamy, S., Kouichi, S., Stanimirović, P.S., Sahoo, J.K. (eds) Proceedings of the Ninth International Conference on Mathematics and Computing. ICMC 2023 2023. Lecture Notes in Networks and Systems, vol 697. Springer, Singapore. https://doi.org/10.1007/978-981-99-3080-7_22  

3. Verma, R., Kumar, S. (2022). Temperature Distribution in Living Tissue with Two-Dimensional Parabolic Bioheat Model Using Radial Basis Function. In: Ray, S.S., Jafari, H., Sekhar, T.R., Kayal, S. (eds) Applied Analysis, Computation and Mathematical Modelling in Engineering. Lecture Notes in Electrical Engineering, vol 897. Springer, Singapore. https://doi.org/10.1007/978-981-19-1824-7_24  

4. Gupta R., Kumar S. (2021) Solution of Variable-Order Space Fractional Bioheat Equation by Chebyshev Collocation Method. In: Awasthi A., John S.J., Panda S. (eds) Computational Sciences - Modelling, Computing and Soft Computing. CSMCS 2020. Communications in Computer and Information Science, vol 1345. Springer, Singapore. https://doi.org/10.1007/978-981-16-4772-7_11 

5. Bansu H., Kumar S. (2021) Meshless Method for Numerical Solution of Fractional Pennes Bioheat Equation. In: Lim C.T., Leo H.L., Yeow R. (eds) 17th International Conference on Biomedical Engineering. ICBME 2019. IFMBE Proceedings, vol 79. Springer, Cham. https://doi.org/10.1007/978-3-030-62045-5_2 

6. Bansu H., Kumar S. (2020) Numerical Solution of Space and Time Fractional Advection–Diffusion Equation by Meshless Approach. In: Bhattacharyya S., Kumar J., Ghoshal K. (eds) Mathematical Modeling and Computational Tools. ICACM 2018. Springer Proceedings in Mathematics & Statistics, vol 320. Springer, Singapore. https://doi.org/10.1007/978-981-15-3615-1_16 

7. Saw V., Kumar S. (2019) The Approximate Solution for Multi-term the Fractional Order Initial Value Problem Using Collocation Method Based on Shifted Chebyshev Polynomials of the First Kind. In: Chandra P., Giri D., Li F., Kar S., Jana D. (eds) Information Technology and Applied Mathematics. Advances in Intelligent Systems and Computing, vol 699. Springer, Singapore. https://doi.org/10.1007/978-981-10-7590-2_4 

8. Kumar S., Singh S. (2018) Numerical Study on Biological Tissue Freezing Using Dual Phase Lag Bio-Heat Equation. In: Mondaini R. (eds) Trends in Biomathematics: Modeling, Optimization and Computational Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-91092-5_19 

9. Mathematical modeling of thawing problem in skin and subcutaneous Tissue, in C.T. Lim and J.C.H. Goh (Eds.): WCB 2010, IFMBE Proceedings 31, (2010) pp. 1611–1614, (with V. K. Katiyar)  https://doi.org/10.1007/978-3-642-14515-5_410