Department of Mathematics

Journal Paper(s):

  1. M. Farooq Khan, H. Alrabaiah, S. Ullah, M. Altaf Khan, M. Farooq, Mustafa bin Mamat, M. Imran Asjad , (2021), "A new fractional model for vector-host disease with saturated treatment function via singular and non-singular operators" , in Alexandria Engineering Journal , February 2021 , 60 ( 1) , 629-645 
  2. Syed Azhar Ali Shah, Muhammad Altaf Khan, Muhammad Farooq, Saif Ullah, Ebraheem O. Alzahrani , (2020), "A fractional order model for Hepatitis B virus with treatment via Atangana-Baleanu derivative" , in Physica A: Statistical Mechanics and its Applications , 538  
  3. MA Khan, SAA Shah, S Ullah, KO Okosun and M Farooq , (2020), "OPTIMAL CONTROL ANALYSIS OF THE EFFECT OF TREATMENT, ISOLATION AND VACCINATION ON HEPATITIS B VIRUS" , in Journal of Biological Systems , 18/06/2020   [ Download ]
  4. Saif Ullah, M Farooq Khan, Syed Azhar Ali Shah, Muhammad Farooq, M Altaf Khan & Mustafa Bin Mamat , (2020), "Optimal control analysis of vector-host model with saturated treatment" , in The European Physical Journal Plus , 135 ( 10) ,   [ Download ]
  5. S. Ullah, M. A. Khan, M. Farooq, Z. Hammouch and D. Baleanu , (2020), "A fractional model for the dynamics of Tuberculosis infection using Caputo-Fabrizio derivative" , in Discrete and Continuous Dynamical Systems - Series S , June 2020 , 13 ( 3) ,  
  6. Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq and Ebraheem O. Alzahrani , (2020), "A fractional model for the dynamics of tuberculosis (TB) using Atangana-Baleanu derivative" , in Discrete & Continuous Dynamical Systems Series-S , 13 ( 3) ,  
  7. Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq, Taza Gul and Fawad Hussain , (2020), "A fractional order HBV model with hospitalization" , in Discrete & Continuous Dynamical Systems Series-S , 13 ( 3) ,  
  8. Fatmawati, Muhammad Altaf Khan, Muftiyatul Azizah, Saif Ullah , (2019), "A fractional model for the dynamics of competition between commercial and rural banks in Indonesia" , in Chaos, Solitons & Fractals , 122  
  9. Tahir Hussain, Fawad Khan , (2019), "CONFORMAL RICCI COLLINEATIONS OF STATIC SPACE-TIMES WITH MAXIMAL SYMMETRIC TRANSVERSE SPACES" , in Theoretical and Mathematical Physics , 198 ( 3) , 463 - 474 
  10. Fawad Khan, Tahir Hussain, Ashfaque Hussain Bokhari and Sumaira Saleem Akhtar , (2019), "Non-Static Spherically Symmetric Spacetimes and their Conformal Ricci Collineations" , in Arabian Journal of Mathematics  
  11. S. Ullah, M. A. Khan and M. Farooq , (2019), "Mathematical Modelling Approach to Hepatitis B virus with Vaccination and optimal control" , in International Journal of Ecology and developments , 34 ( 3) , 69-81 
  12. Saif Ullah, Muhammad Altaf Khan and Jose Francisco Gomez Aguilar , (2019), "Mathematical formulation of hepatitis B virus with optimal control analysis" , in Optim Control Appl Meth.  
  13. Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq & Taza Gul, Available online 1st April 2019. , (2019), "Modeling and analysis of Tuberculosis (TB) in Khyber Pakhtunkhwa Pakistan" , in Mathematics and Computers in Simulation , 01/11/2019 , 165  
  14. MA Khan, M Ahmad, S Ullah, M Farooq & T Gul , (2019), "Modeling the transmission dynamics of tuberculosis in Khyber Pakhtunkhwa Pakistan" , in Advances in Mechanical Engineering , 11 ( 6) , 1-13 
  15. Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq , (2019), "Mathematical modelling of Hepatitis B infection with vaccination and optimal control interventions" , in Journal of Computational Methods in Sciences and Engineering  
  16. Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq , (2018), "A new fractional model for the dynamics of Hepatitis B virus using Caputo-Fabrizio derivative" , in European Physical Journal Plus   [ Download ]
  17. Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq , (2018), "A fractional model for the dynamics of TB virus" , in Chaos, Solitons & Fractals , 116  
  18. Muhammad Altaf Khan, Saif Ullah, Muhammad Farooq , (2018), "A new fractional model for tuberculosis with relapse via Atangana-Baleanu derivative" , in Chaos, Solitons & Fractals , 116  
  19. Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq , (2018), "Modeling and analysis of fractional HBV model with Atangana-Baleanu derivative" , in Eur. Phys. J. Plus , 2018  
  20. Tahir Hussain, Fawad Khan, Ashfaque H. Bokhari and Sumaira Saleem Akhtar , (2018), "Classification of Kantowski-Sachs Metric via Conformal Ricci Collineations" , in International journal of geometric methods in modern physics , 15  
  21. Imran Aziz, Imran Khan , (2018), "Numerical Solution of Diffusion and Reaction-Diffusion Partial Integro-Differential Equations" , in Int. J. Comp. Meth. , 15 ( 6) ,  
  22. Tahir Hussain, Sumaira Saleem Akhtar , (2018), "Energy Conditions and Conservation Laws in LTB Metric via Noether Symmetries" , in European Physical Journal C , 78  
  23. Sumaira Saleem Akhtar, Tahir Hussain, Ashfaque Hussain Bokhari , (2018), "Positive Energy Condition and Conservation Laws in Kantowski-Sachs Spacetime via Noether Symmetries" , in Symmetry , 10 ( 712) ,  
  24. Tahir Hussain and Muhammad Farhan , (2018), "Proper Conformal Killing Vectors in Kantowski-Sachs Metric" , in Communications in Theoretical Physics , 69 ( 393) ,  
  25. Sumaira Saleem Akhtar, Tahir Hussain, Ashfaque Hussain Bokhari and Fawad Khan , (2018), "Conformal Collineations of the Ricci and Energy-Momentum Tensors in Static Plane Symmetric Spacetimes" , in Theoretical and Mathematical Physics , 195 ( 595) ,  
  26. Tahir Hussain, Sumaira Saleem Akhtar and Fawad Khan , (2018), "Homothetic Ricci Collineations of Non-Static Spherically Symmetric Spacetimes with Perfect Fluid Matter" , in Modern Physics Letters A , 33  
  27. Tahir Hussain and Sumaira Saleem Akhtar , (2018), "Homothetic Ricci Collineations in Non- Static Plane Symmetric Spacetimes with Perfect Fluid Matter" , in International Journal of Geometric Methods in Modern Physics , 15  
  28. Muhammad Sajjad Ali Khan, Saleem Abdullah, Muhammad Yousaf Ali, Iqtadar Hussain and Muhammad Farooq , (2018), "Extension of TOPSIS method based on Choquet integral under interval-valued Pythagorean fuzzy environment" , in Journal of Intelligent and Fuzzy Systems , 34 ( 1) , 267-282 
  29. M. Adil Khan, T. Ali, S. S. Dragomir and M. Z. Sarikaya , (2017), "Hermite-Hadamard type inequalities for conformable fractional integrals" , in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas  
  30. Yu-Ming Chu, M. Adil Khan, T. Ali and S. S. Dragomir , (2017), "Inequalities for a-fractional differentiable functions" , in J. Inequal. Appl. , 93  
  31. M. Adil Khan, J. Khan, and J. Pe?ari? , (2017), "Generalizations of Sherman's inequality by Montgromey identity" , in Electronic Journal of Mathematical Analysis and Applications , 5 ( 1) , 1 - 16 
  32. Imran Aziz, Siraj-ul-Islam, Nadeem Haider , (2017), "Meshless and multi-Resolution collocation techniques for steady state interface models" , in International Journal of Computational Mathematics,  
  33. Fawad Khan, Tahir Hussain and Sumaira Saleem Akhtar , (2017), "Conformal Ricci Collineations in LRS Bianchi type V Spacetimes with Perfect Fluid Matter" , in Modern Physics Letters A , 31  
  34. Tahir Hussain, Suhail Khan, Ashfaque H. Bokhari and Gulzar Ali Khan , (2017), "Proper Conformal Killing Vectors in Static Plane Symmetric Spacetimes" , in Theoretical and Mathematical Physics , 191 ( 620) ,  
  35. Imran Aziz and Imran Khan , (2017), "Numerical Solution of Partial Integro-differential Equations of Diffusion Type" , in Math. Prob. Eng.  
  36. M. Adil Khan, Gilda Pecaric and Josip Pecaric , (2017), "Bounds for Shannon and Zipf-mandelbrot entropies" , in Mathematical Method in Applied Sciences  
  37. Tahir Hussain and Waqas Rahim , (2017), "Homothetic Matter Collineations of LRS Bianchi type I Spacetimes," , in Modern Physics Letters A , 32  
  38. Imran Aziz, Siraj-ul-Islam, Muhammad Asif , (2017), "Haar wavelet collocation method for three-dimensional elliptic partial differential equations" , in Journal of Computer and Mathematics with Application , 73  
  39. Suhail Khan, Tahir Hussain and Gulzar Ali Khan , (2017), "Teleparallel Conformal Killing Vector Fields of LRS Bianchi type V Spacetimes in Teleparallel Gravity" , in International Journal of Geometric Methods in Modern Physics , 14  
  40. Fawad Khan, Tahir Hussain and Sumaira Saleem Akhtar , (2017), "Conformal Ricci Collineations in LRS Bianchi type V Spacetimes with Perfect Fluid Matter" , in Modern Physics Letters A , 32  
  41. Tahir Hussain, Sumaira Saleem Akhtar and Fawad Khan , (2017), "Classification of Locally Rotationally Symmetric Bianchi-I Spacetimes using Conformal Ricci Collineations" , in Theoretical and Mathematical Physics , 193  
  42. M. Adil Khan, Naveed Latif, J. Pecaric , (2016), "Generalizations of majorization inequality via Lidstone's Polynomial and their applications" , in Communications in Mathematical Analysis , 19 ( 2) , 101 - 122 
  43. Imran Aziz, Rohul Amin , (2016), "Numerical solution of a class of delay differential and delay partial differential equations via Haar wavelet" , in Applied Mathematical Modelling , 40  
  44. Imran Aziz, Siraj-ul-Islam , (2016), "An Efficient Modified Haar Wavelet Collocation Method for Numerical Solution of Two-Dimensional Elliptic PDEs" , in , Differential Equations and Dynamical Systems  
  45. Tahir Hussain, Aisha Musharaf and Suhail Khan , (2016), "Ricci inheritance collineations in Kantowski-Sachs spacetimes" , in International Journal of Geometric Methods in Modern Physics , 13  
  46. Tahir Hussain, Sumaira Saleem Akhtar, Ashfaque H. Bokhari and Suhail Khan , (2016), "Ricci inheritance collineations in Bianchi type II spacetime" , in Modern Physics Letters A , 31  
  47. Suhail Khan, Tahir Hussain and Gulzar Ali Khan , (2016), "A note on teleparallel conformal Killing vector fields in plane symmetric non static spacetimes" , in International Journal of Geometric Methods in Modern Physics , 13  
  48. Suhail Khan, Tahir Hussain, Ashfaque Hussain Bokhari and Gulzar Ali Khan , (2016), "Conformal Killing Vectors in LRS Bianchi type V Spacetimes" , in Communications in Theoretical Physics , 65 ( 315) ,  
  49. Akbar Zada, Shah Faisal and Yongjin Li , (2016), "On the Hyers-Ulam Stability of First-Order Impulsive Delay Differential Equations" , in Journal of Function Spaces  
  50. T. Li, A. Zada, and S. Faisal , (2016), "Hyers-Ulam stability of nth order linear differential equations" , in The Journal of Nonlinear Science and Applications , 9 ( 5) , 2070-2075 
  51. Akbar Zada, Tongxing Li, Samreen Ismail and Omar Shah , (2016), "Exponential Dichotomy of Linear Autonomous Systems Over Time Scale" , in Differential Equations and Applications , 8 ( 2) , 123-134 
  52. Tahir Hussain, Sumaira Saleem Akhtar and Suhail Khan , (2015), "Ricci inheritance collineations in Bianchi type I spacetimes" , in European Physical Journal Plus , 2015 , 44 ( 130) ,  
  53. Rahim Shah, Akbar Zada, and Ishfaq Khan , (2015), "Some Fixed Point Theorems of Integral Type Contraction in Cone b-metric Spaces" , in Turkish Journal of Analysis and Number Theory , 3 ( 6) , 165-169 
  54. Suhail Khan, Tahir Hussain, Gulzar Ali Khan and Amjad Ali , (2015), "A Note on Teleparallel Killing Symmetries in Three Dimensional Circularly Symmetric Static Spacetime" , in International Journal of Theoretical Physics , 54 ( 2969) ,  
  55. Suhail Khan, Tahir Hussain, Ashfaque Hussain Bokhari and Gulzar Ali Khan , (2015), "Conformal Killing Vectors of Plane Symmetric Four Dimensional Lorentzian Manifolds" , in European Physical Journal C , 75 ( 523) ,  
  56. Muhammad Farooq and Abdellah Salhi , (2015), "A new Lanczos-type Algorithm for solving linear systems of equations" , in Journal of Prime Research in Mathematics , 10  
  57. Zakir Ullah, Muhammad Farooq and Abdellah Salhi , (2015), "A19/B6: A New Lanczos-type Algorithm and its Implementation" , in Journal Of Prime Research in Mathematics , 11  
  58. Muhammad Farooq, Abdellah Salhi , (2014), "A Switchting Approach to avoid Breakdown in Lanczos-type Algorithms" , in Applied Mathematics & Information Sciences , 2014 , 8 ( 5) ,  
  59. Suhail Khan, Tahir Hussain and Gulzar Ali Khan , (2014), "Conformal Killing symmetries of Plane-Symmetric Static Spacetimes in Teleparallel Theory of Gravitation" , in European Physical Journal Plus , 129 ( 228) ,  
  60. Suhail Khan, Tahir Hussain and Gulzar Ali Khan , (2014), "A Note on Teleparallel Lie Symmetries using Non Diagonal Tetrad" , in Romanian Journal of Physics , 59 ( 488) ,  
  61. Imran Aziz, Siraj-ul-Islam, Fawad Khan , (2014), "A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations" , in Journal of Computational and Applied Mathematics , 272  
  62. Siraj-ul-Islam, Imran Aziz, A.S. Al-Fhaid , (2014), "An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders" , in Journal of Computational and Applied Mathematics , 260  
  63. Muhammad Farooq, Abdellah Salhi , (2013), "A Preemptive Restarting Approach to Beating the Inherent Instability of Lanczos-type Algorithms" , in Iranian Journal of Science & Technology, Transaction A-Science , 2013 , 37 ( 3.1) , 349 - 358 
  64. Saif Ullah, Muhammad Farooq and Abdellah Salhi , (2013), "An alternative derivation of a new Lanczos-type algorithm for system of linear equations" , in Punjab University Journal of Mathematics , 45  
  65. Siraj-ul-Islam, Imran Aziz, A.S. Al-Fhaid, Ajmal Shah , (2013), "A numerical assessment of parabolic partial differential equations using Haar and Legendre wavelets" , in Applied Mathematical Modelling , 37 ( 23) , 9455-9481 
  66. Siraj-ul-Islam, Imran Aziz, Muhammad Fayyaz , (2013), "A new approach for numerical solution of integrodifferential equations via Haar wavelets" , in International Journal of Computer Mathematics , 90 ( 9) , 1971-1989 
  67. Imran Aziz, Siraj-ul-Islam , (2013), "New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets" , in Journal of Computational and Applied Mathematics , 239  
  68. Imran Aziz, Siraj-ul-Islam, Bozidar Sarler , (2013), "Wavelet collocation methods for the numerical solution of elliptic BV problems" , in Applied Mathematical Modelling , 37 ( 3) , 676-694 
  69. Muhammad Farooq and Abdellah Salhi , (2012), "New Recurrence Relationships between Orthogonal Polynomials which Lead to New Lanczos-type Algorithms" , in Journal Of Prime Research in Mathematics , 8  
  70. Siraj-ul-Islam, Imran Aziz, Wajid Khan , (2012), "Numerical integration of multi-dimensional highly oscillatory, gentle oscillatory and non-oscillatory integrands based on wavelets and radial basis functions" , in Engineering Analysis with Boundary Elements , 36  
  71. Muhammad Farooq, Abdellah Salhi , (2011), "Improving the Solvability of Ill-conditioned Systems of Linear Equations by Reducing the Condition Number of their Matrices" , in J. Korean Math. Soc. , 01/09/2011 , 48 ( 5) , 939 - 952 
  72. Imran Aziz, Siraj-ul-Islam, Wajid Khan , (2011), "Quadrature rules for numerical integration based on Haar wavelets and hybrid functions" , in Computers and Mathematics with Applications , 61  
  73. Siraj-ul-Islam, Bozidar Sarler, Imran Aziz, Fazal Haq , (2011), "Haar wavelet collocation method for the numerical solution of boundary layer fluid flow problems" , in International Journal of Thermal Sciences , 50  
  74. Fazal Haq, Siraj-ul-Islam, Imran Aziz , (2011), "Numerical solution of singularly perturbed two-point BVPs using non-uniform Haar Wavelets" , in International Journal for Computational Methods in Engineering Science & Mechanics , 12 ( 4) , 168-175 
  75. M. Adil Khan, J. Pecaric , (2010), "Improvement and reversion of Slater's inequality and related results" , in J. Inequal. and Appl.  
  76. Siraj-ul-Islam, Imran Aziz and Fazal Haq , (2010), "A comparative study of numerical integration based on Haar wavelets and hybrid functions" , in A comparative study of numerical integration based on Haar wavelets and hybrid functions , 59 ( 6) , 2026-2036 
  77. M. Adil Khan, M. Anwar, J. Jaksetic and J. Pecaric , (2009), "On some improvements of the Jensen inequality with some applications" , in J. Inequal. and Appl.  
  78. C. Buse, Akbar Zada , (2009), "Dichotomy and bounded-ness of solutions for some discrete Cauchy problems" , in Operator Theory advances and applications , 203  
  79. Akbar Zada , (2008), "A characterization of dichotomy in terms of boundedness of solutions for some Cauchy problems" , in Electronic Journal of Differential Equations , 94  

Conference Paper(s):

  1. Imran Aziz, Rohul Amin and Juri Majak, (2016), "Numerical solution of a class of fractional delay differential equations via Haar wavelet" , in 11th International DAAAM Baltic Conference (Industrial Engineering) , April 20-26, 2016, Tallinn, Estonia  
  2. Imran Aziz, (2014), "Numerical solution of system of nonlinear Fredholm and Volterra integral equations using Haar wavelet" , in International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2014) , November 6-9, 2014, Antalya, Turkey  
  3. Imran Aziz and Siraj-ul-Islam, (2014), "An improved wavelet collocation method for numerical solution of twodimensional elliptic partial differential equations" , in Third International Conference for Computational Method for Thermal Problems , June 2-4, 2014, Lake Bled, Slovenia  
  4. Imran Aziz and Siraj-ul-Islam, (2013), "An improved method based on Haar wavelets for numerical solution of nonlinear integral equations" , in International conference on Modelling and Simulation 2013 (ICOMS-2013) , Islamabad, Pakistan