Nonlinear Waves

Research interest:

One of the most common types of solutions for nonlinear wave equations is solitons which play a crucial role in nonlinear physical phenomena research. We are, in particular,  interested in solitons in optical fibers governed by Nonlinear Schrodinger (NLS) type equations. We study the existence conditions and modulation instability of the perturbed NLSEs.

Publications:

Kaltham K. Al-Kalbani, K.S. Al-Ghafri, E.V. Krishnan, Anjan Biswas, Pure-cubic optical solitons by Jacobi's elliptic function approach, Optik, 243(2021)167404. (13 pages)

Kaltham K. Al-Kalbani, K.S. Al-Ghafri, E.V. Krishnan, Anjan Biswas,  Solitons and modulation instability of the perturbed Gerdjikov-Ivanov equation with spatio-temporal dispersion,  Chaos, Solitons and Fractals, 153(2021)111523. (8 pages)

Bio-Mathematics

Research interest:

We studied a deterministic predator-prey compartmental model to investigate the impact of their speeds on their interactions. Prey hide themselves in a refuge area and come out of this area when predation pressure decline. To avoid predation, prey can limit their speed. For small antipredator behavior, we examined that prey mortality increases when either predator prey velocity increases while raising antipredator behavior increases prey density. We proved that predator free equilibrium is globally asymptotically stable and coexisting equilibrium will be globally stable under a certain conditions. We find that trans-critical bifurcations occurs for predator free equilibrium at the certain value of the death rate of the predator.

Publications:

Anuraj Singh, Krishna Pada Das, Binayak Nath, Somnath Maiti, Qamar Jalil Ahmad Khan,” Stabilization of chaos in an eco-epidemiological model with allee effect in the prey population” Nonlinear Studies Vol. 28, No. 2, pp. 689-703, 2021

Greenhalgh, D; Khan, Q. J. A; Al-Kharousi, F. A.,”Eco-epidemiological model with fatal disease in prey”, Nonlinear Analysis: Real World Applications, Vol.53, June 2020 Article No.103072.

https://doi.org/10.1016/J.NONRWA.2019. 

Difference Equations

Research interest:

I did my PhD in Difference Equations and since then I explored other topics related and close to it. I continued my research in the area of Difference Equations and in other related areas at well. I was involved in several research projects such as Fractional Derivatives, E-Learning and Stability of solutions in certain Partial differential equation problem occurred in Fractured Rock Reservoir. Currently, I am exploring the area of Epidemiology with my colleagues.

Publications:

A. Al-Ghassani and R G Halburd, Height growth of solutions and a discrete Painlev equation, IOP publishing, London Mathematical Society, Nonlinearity Vol. 28, No. 7 (2015) 2379-2396, DOI:10.1088/0951-7715/28/7/2379, URL: http://iopscience.iop.org/0951-7715/28/7/2379/pdf/0951-7715_28_7_2379.pdf.

Asma S. Al-Ghassani and Ziyad AlSharawi, The effect of maps permutation on the global attractor of a periodic Beverton-Holt model, Applied Mathematics and Computation, Volume 370, (2020), pages 124905, ISSN 0096-3003, DOI https://doi.org/10.1016/j.amc.2019.124905. http://www.sciencedirect.com/science/article/pii/S0096300319308975

Applied Mathematics

Research interest:

Algebraic Methods in Systems Theory and Control in particular Multidimensional Systems Theory, Symbolic Computation, Reduction and Simplification of Linear Functional Systems, Multivariate Matrix Factorization, System Equivalence, Applications to Linear Repetitive Processes and Circuit Theory.

 Publications:

Boudellioua, M.S. and Quadrat, A., "Serre's Reduction of Linear Functional Systems", Mathematics in Computer Science (Springer), 2010, 4, 2-3, 289--312.

Boudellioua, M.S. and Cluzeau, T., "On the connections between two classical notions of multidimensional system equivalence", International Journal of Control (Taylor and Francis), 2021, 94, 11, 3046—3053

Functional Analysis and Operator Theory

Research interest:

Operators on Function Spaces. More precisely: Exploring Composition Operators, Multiplication Operators, Weighted Composition Operators, Weighted Differentiation Composition Operators, and Isometries on Spaces of Analytic Functions, Spaces of Continuous Functions, Spaces of Measureable Functions and their Applications.

Publications:

Manhas, Jasbir S.; Al Ghafri, Mohammed S. Sums of weighted differentiation composition operators from weighted Bergman spaces to weighted Zygmund and Bloch-type spaces. Adv. Oper. Theory 6 (2021), no. 3, Paper No. 51, 43 pp. 

Al Ghafri, Mohammed S.; Manhas, Jasbir S. On Stević-Sharma operators from weighted Bergman spaces to weighted-type spaces. Math. Inequal. Appl. 23 (2020), no. 3, 1051–1077.

Fractional Calculus

Research interest: Fractional Differential Equations: Existence, Non-Existence, Stability of solutions and applications.

Publications:

1M Kirane, AZ Fino, S Kerbal, Nonexistence of global positive solutions for p-Laplacian equations with non-linear memory, Fractal and Fractional, 2021, 5 (4), 189.

S Kerbal, NE Tatar, Exponential stabilization of a neutrally delayed viscoelastic Timoshenko beam, Turkish Journal of Mathematics, 2019,  43 (2), 595-611

Computational PDEs

Research interest:

Fractional-order PDEs with non-smooth data, Semi-linear parabolic problems, Mixed finite element methods, Stochastic differential equations

Publications:

Samir Karaa, Positivity of discrete time-fractional operators with applications to phase-field equations, SIAM Journal Numer. Anal., 59 (2021), no. 4, pp. 2040-2053.

Mariam Al-Maskari and Samir Karaa, Numerical Approximation of semilinear subdiffusion equations with nonsmooth initial data, SIAM J. Numer. Anal., 57 (2019), no. 3, pp. 1524-1544.

Fluid Dynamics

Research interest:

My general field of research interest is Fluid Dynamics modeling through the differential equations, particularly in the field of Nanofluidic phenomenon (applications to nanoscience), Heat and Mass Transfer (applications to industry), Magnetohydrodynamics (applications to geophysics), Transport in Porous Media (applications to underground water, petroleum industry), Bio-Fluid Flows (applications to blood flows).

Publications:

M. M. Rahman, M. Z. Saghir and I. Pop: Free convective heat transfer efficiency in Al2O3-Cu/water hybrid nanofluid inside a rectotrapezoidal enclosure, International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32(1), 196-218, 2022.

M. M. Rahman, I. Pop and M. Z. Saghir: Steady free convection flow within a titled nanofluid saturated porous cavity in the presence of a sloping magnetic field energized by an exothermic chemical reaction, International Journal of Heat and Mass Transfer, vol. 129, pp. 198-211, 2019.

Mathematical Biology

Research interest:

Developing mathematical models to understand the dynamics of predator-prey interactions under different assumptions and factors i.e., refuge, fear, cooperation and spatial distribution. Developing mathematical models for the dynamics of communicable diseases via different routes i.e., direct, through vector and environmental transmissions. Parameter’s estimation from real data for better understanding of disease progression. Applying optimal control theory for disease control.

Publications:

Fatma Almusalhi, Nasser Al-Salti, Ibrahim M. Elmojtaba, Velmurugan Gandhi. (2021). SIR Model with Time-Varying Contact Rate. International Journal of Biomathematics. DOI:  10.1142/S1793524521500170

Nasser S. Al-Salti, Fatma Al-Musalhi, Velmurugan Gandhi, Mariam Al-Moqbali and Ibrahim M. Elmojtaba. (2021). Dynamical analysis of a prey-predator model incorporating a prey refuge with variable carrying capacity. Ecological Complexity. Vol 45, Article number 100888.

Computational mathematics

Research interest:

Fractional Calculus, Numerical Approximation of fractional differential equations, Non-polar spherical coordinate systems and its harmonics.

Publications:

[1] Gunarathna, W. A., H. M. Nasir, and W. B. Daundasekera. "An explicit form for higher order approximations of fractional derivatives." Applied Numerical Mathematics 143 (2019): 51-60.

[2] Nasir, H.M. and Nafa, K. Algebraic construction of a third order difference approximations for fractional derivatives and applications. ANZIAM Journal, 59 (2017): C254-C269.

Mathematics

Research interest: Algebra, Ordered Semigroup Theory, Algebraic Semigroup Theory.

Publications:

2022 - Ordered Regular Pointed Semigroups with Biggest Associates, Palestine Journal of Mathematics, Vol. 11(1), (2022), 270-279.

2021 - Boolean Zero Square (BZS) Semigroups, SQU Journal for Science, 26(1), 31-29.

Commutative Algebra

Research interest:

Gröbner bases of ideals. Number of generators of powers of ideals. The reduction number of monomial ideals. Normal Ideals. The Ratliff-Rush of closure ideals. Cover ideals of graphs. Superficial ideals.

Publications: 

 Al-Ayyoub, M. Nasernejad, L. Roberts, K. Khashyarmanesh, and V.C. Quiñonez, Some Results on the Normality of Square-free Monomial ideals and Cover Ideals of Graphs, Mathematica Scandinavica, 127  (2021); 441-457.

Al-Ayyoub, Results on the Behavior of the Ratliff-Rush Operation and the Depth of the Associated Graded Ring, Communications in Algebra, 49 (8) (2021); 3447-3456.

I. Al-Ayyoub and M. Nasernejad, Monomial Ideals with Tiny Squares and Freiman Ideals, Czechoslovak Mathematical Journal, 71 (146) (2021); 847-864.

Group Theory

Research interest: Combinatorial and Geometric Group Theory, Algebraic Geometry over Groups, Symbolic Dynamics over Groups, Polyadic Groups, Model Theoretical Problems in Group Theory, Lie Algebras and Generalizations

Publications:

Compactness conditions in universal algebraic geometry,   Algebra and Logic, 2016.

Existentially closed structures and some embedding theorems, Mathematical Notes, 2017.

Wavelet Analysis, Integral Transforms, Frame Theory

Research interest:

Fourier transforms, Hilbert transforms, Boas transforms, Zak transforms, wavelet transforms, wavelet packets and their applications. Study of Gabor systems for oversampling schemes. Uncertainty principles and Balian-Low theorems. Frame theory and its applications in the field of signal processing and sampling theory.

Publications:

N. Khanna , J. H. Arredondo, L. Kathuria and S. K. Kaushik, An improved one point quadrature formula, Numer. Funct. Anal. Optim. 42 (2021), no. 2, 123-131.

N. Khanna , S. K. Kaushik and S. V. Djordjević, An interplay between parameter (p,q)-Boas transform and linear canonical transform, J. Pseudo-Differ. Oper. Appl. 12 (2021), no. 3, Paper No. 46, 19 pp.

N. Khanna , S. K. Kaushik and A. M. Jarrah, Some remarks on Boas transforms of wavelets, Integ. Transf. Special Funct. 31 (2020), no. 2, 107-117.

Applied Mathematics

Research interest:

Mathematical modeling study of dispersion of wastewater effluent disposal into the ocean through marine outfall systems in the far-field, which ranges from steady discharges via single port to multiport diffusers. Other factors included in the model are oscillating tidal flows, seabed depth profiles, effluent decay and adsorption by sediments. The software package CORMIX is used to study the dispersion of effluents discharged in the near field.

Publications:

Purnama, A., Al Maamari, H.A. & Balakrishnan, E. (2017) Optimal Outfall Systems for Nearshore Effluent Discharges on Eroded Sandy Beaches, Journal of Coupled Systems and Multiscale Dynamics, 5(2-4): 217–224 doi:10.1166/jcsmd.2017.1134

Al-Kasbi, A. & Purnama, A. (2021) Behaviour of Effluent Discharged into Shallow Coastal Waters under the Influence of Spring-Neap Tidal Currents, Environmental Fluid Mechanics, doi.org/10.1007/s10652-021-09826-1