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صفحة جديدة 1
Fixed point theory and applications, Best approximation theory, Operator theory, topological-algebraic structures in functional analysis, Existence theory of fractional differential equations, stability and instability properties of dynamical systems, Impulsive hybrid state dependent delay systems, Nonlinear boundary value problems, Analytic approximate methods, stability theory, Mathematical modeling and numerical simulation of partial differential equations with applications in Biomathematics, Blood flow problems, Newtonian and Non-Newtonian fluid mechanics, and wave motion.
Projects
Projects Completed in 2011
1. Some Problems of Fractional Calculus and Real world Applications
(Investigators: Bashir Ahmad Mohammed, Ahmed Alsaedi, Juan .J. Nieto (Spain), Mustafa El-Shahed) .
2. Fractional Differential Inclusions: Fixed Point Approaches (Investigators: Dr. Bashir Ahmad Mohammed, Naseer Shahzad, Ahmed Alsaedi, Ravi P. Agarwal(USA)).
3. Interaction of Peristalsis with Heat Transfer and Magnetohydrodynamics (Investigators: Shabab Ahothuali, Saleem Asghar (PAK), Tasawar Hayat (PAK), Adnan Alhomaidan).
4. Metric Fixed Point Theory and Applications (Investigators: Abdul Latif Noor Muhammad, Mohammed Amine Khamsi (USA), Hamed Al-Sulami, Nawab Hussain).
Projects in Progress 2012
1. Numerical analysis of PDEs and Scientific Computing (Investigators: Ahmed Alsaedi, Franco Brezzi (HiCi-Italy), Ebraheem alzahrani, Bashir Ahmad).
Proposed Research Projects
• A Study of Fractional Differential Equations on Infinite Domain
• Nonlinear Third-Order Boundary Value Problems with Integral Boundary Conditions
• Some fundamental flows characterizing realistic fluids in a porous media
• Transient growth and pattern selection in biological and related
• Mathematical Analysis of the spread of dengue fever
• Control and possibly eradication of HCV disease
Selected Recent Publications (2011-2012)
1. Bashir Ahmad, Juan J. Nieto, Ahmed Alsaedi, Moustafa El-Shahed, A study of nonlinear Langevin equation involving two fractional orders in different intervals, Nonlinear Analysis: Real World Applications 13 (2012) 599–606.
2. Guotao Wang, Bashir Ahmad and Lihong Zhang, Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order, Nonlinear Analysis 74 (2011) 792–804.
3. Bashir Ahmad, On nonlocal boundary value problems for nonlinear integro-differential equations of arbitrary fractional order, Results in Mathematics, DOI: 10.1007/s00025-011-0187-9, in press.
4. Ravi P. Agarwal and Bashir Ahmad, Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions, Computers and Mathematics with Applications, Volume 62, Issue 3, August 2011, Pages 1200-1214.
5. Bashir Ahmad and Sotiris K. Ntouyas, Boundary value problems for q-difference inclusions, Abstract and Applied analysis, Volume 2011, Article ID 292860, 15 pages.
6. Bashir Ahmad, Juan J. Nieto, Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions, Boundary Value Problems 2011, 2011:36 doi:10.1186/1687-2770-2011-36, 9 pages.
7. Bashir Ahmad and Juan J. Nieto, Existence of solutions for impulsive anti-periodic boundary value problems of fractional order, Taiwanese Journal of Mathematics 15 (2011), 981-993.
8. E.T. Karimov, J.J. Nieto, he Dirichlet problem for a 3D elliptic equation with two singular coefficients, Comput. Math. Appl. 62 (2011), no. 1, 214-224.
9. D. Băleanu, O. Mustafa, R.P. Agarwal, Asymptotic integration of $(1+\alpha)$-order fractional differential equations. Comput. Math. Appl. 62 (2011), no. 3, 1492-1500.
10. Juntao Sun, Haibo Chen, Juan J. Nieto, On ground state solutions for some non-autonomous Schrödinger–Poisson systems, J. Differential Equations (2012) doi.org/10.1016/j.jde.2011.12.007, in press.
11. T. Hayat, S. A. Shehzad and A. Alsaedi, On three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions, International Journal of the Physical Sciences (IJPS), in press.
12. Moustafa El-Shahed and Ahmed Alsaedi, The Fractional SIRC Model and Influenza A, Mathematical Problems in Engineering, Volume 2011, Article ID 480378, 9 pages doi:10.1155/2011/480378.
13. Ahmed Alsaedi and Mohammed H Aqlan, On nonlocal three-point boundary value problems of Duffing equation with mixed nonlinear forcing terms, Boundary Value Problems 2011 2011:47, 11 pages.
14. Najma Saleem, T. Hayat and A. Alsaedi, Effects of induced magnetic field and slip condition on peristaltic transport with heat and mass transfer in a non-uniform channel, International Journal of the Physical Sciences (IJPS), in press.
15. Ahmed Alsaedi, Approximation of solutions for second-order $m$-point nonlocal boundary value problems via the method of generalized quasilinearization. Boundary Value Problems, Art. ID 929061 (2011), 17 pp.
16. Bashir Ahmad, Juan J. Nieto, Ahmed Alsaedi, Existence and uniqueness of solutions for nonlinear fractional differential equations with non-separated type integral boundary conditions, Acta Mathematica Scientia 31(2011), 2122-2130
17. R.H. Haghi, Sh. Rezapour and N. Shahzad, Some fixed point generalizations are not real neralizations, Nonlinear Analysis, Theory, Methods & Applications, 74 (2011), 263-272.
18. N. Shahzad and G. Bassindowa, Fixed point theorems for Suzuki-generalized nonexpansive mappings with applications, Journal of Nonlinear and Convex Analysis, (2011), in press.
19. Y. Yao and N. Shahzad, Iterative methods for nonexpansive mappings in Banach spaces, Numerical Functional Analysis Optimization, 32 (2011), 583 - 592.
20. H. K. Pathak and N. Shahzad, A generalization of Nadler's fixed point theorem and its application to nonconvex integral inclusions, Topological Methods in Nonlinear Analysis, (2011), in press.
21. R.P. Agarwal, X. Qin, S.M. Kang, Strong convergence theorems for strongly continuous semigroups of pseudocontractions, Appl. Math. Lett. 24 (2011), no. 11, 1845--1848.
22. A. Latif and Afrah A. N. Abdou, Multivalued generalized nonlinear contractive maps and fixed points, Nonlinear Analysis, 74 (2011), 1436-1444.
23. N. Hussain, M.A. Khamsi and A. Latif, “Common fixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions” Nonlinear Analysis, 74 (2011), 2133-2140.
24. N. Hussain, M.A. Khamsi and A. Latif, Banach operator pairs and common fixed points in hyperconvex metric spaces, Nonlinear Analysis, 74 (2011), 5956-5961.
25. M. A. Khamsi, A. Latif and H. Al-Sulami, KKM and Fan theorems in modular function spaces, Fixed Point Theory and Applications, 2011, 2011:57.
26. N. Hussain, M.A. Khamsi and A. Latif, Banach operator pairs and common fixed points in modular function spaces, Fixed Point Theory and Applications, 2011, 2011:75.
27. M.A. Khamsi, W.M. Kozlowski, “On Asymptotic Pointwise Nonexpansive Mappings in Modular Function Spaces”, Journal of Mathematical Analysis and Applications, 380 (2011) 697-708.
28. R.P. Agarwal, M.A. Khamsi, “Extension of Caristi's Fixed Point Theorem to Vector valued Metric Spaces”, Nonlinear Analysis: Theory, Methods & Applications, 74 (2011) 141-145.
29. N. Hussain and M. H. Shah, KKM mappings in cone b-metric spaces, Computers and Mathematics with Applications, 62(2011), 1677-1684.
30. N. Hussain and M. Abbas, Common fixed point results for two new classes of hybrid pairs in symmetric spaces, Applied Mathematics and Computation, 218 (2011) 542–547.
31. T. Hayat, N. Saleem, S. Asghar, M. S. Alhothuali, A. Alhomaidan, Influence of induced magnetic field and heat transfer on peristaltic transport of a Carreau fluid, Com. Nonlinear Sci. Numerical Simulation, 16 (2011) 3559-3577.
32. T. Hayat, S. Noreen, M. Shabab Alhothuali, S. Asghar, Peristaltic flow under the effects of an induced magnetic field and heat and mass transfer, Int. J. Heat Mass Transfer (2011), doi:10.1016/j.ijheatmasstransfer.2011.09.044, in press.
33. Sadia Hina, Tasawar Hayat, Saleem Asghar, Mohammed Shabab Alhothuali and Adnan Alhomaidan, Magnetohydrodynamic nonlinear peristaltic flow in a compliant walls channel with heat and mass transfer, ASME Journal of Heat Transfer, accepted.
34. T. Hayat, M. Qasim, Radiation and magnetic field effects on the unsteady mixed convection flow of a second grade fluid over a vertical stretching sheet, International Journal for Numerical Methods in Fluids, 66 (2011), 820–832.
35. M. Saleem, S. Asghar, M.A. Hossain, Natural convection flow of micropolar fluid in a rectangular cavity heated from below with cold sidewalls. Math. Comput. Modelling 54 (2011), no. 1-2, 508-518.
36. A. Ahmad, S. Asghar, Flow of a second grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field. Appl. Math. Lett. 24 (2011), no. 11, 1905--1909.
37. M. El-Shahed, M. Gaber, Two-dimensional $q$-differential transformation and its application. Appl. Math. Comput. 217 (2011), no. 22, 9165--9172.
38. M. El-Shahed, W.M. Shammakh, Existence of positive solutions for m-point boundary value problem for nonlinear fractional differential equation. Abstr. Appl. Anal. 2011, Art. ID 986575, 20 pp
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