Research
Research Interests:
- Fractional Differential Equations.
- Computational methods for fractional differential equations
- Flow in Porous Media Models
Journal Articles
K. M. Furati. The solution of the
Riemann problem for a hyperbolic system modeling polymer flooding with
hysteresis. Journal of Mathematical Analysis
and Applications, 206(1), 205-233 1997.
K. M. Furati.
Effects of relative permeability history dependence on two-phase flow in
porous media. Transport in Porous Media,
28:181-203, 1997.
K. M. Furati.
History effects on oil recovery efficiency.
Journal of Petroleum Science and Engineering,
19:295-308, 1998.
M. A.
El-Gebeily and K. M. Furati. On the completeness of the set of eigenvectors
of a certain class of self-adjoint finite difference operators.
IMA Journal of Applied Mathematics,
65(1):29-43, 2000.
K. M. Furati,
M. A. Alsunaidi, and H. M. Masoudi. An explicit finite difference scheme for
wave propagation in nonlinear optical structures.
Applied Mathematics Letters,
14(3):297-302, 2001.
K. M. Furati,
M. A. Alsunaidi, and H. M. Masoudi. Simulation of beam propagation in
second-order nonlinear optical media. Microwave and Optical Technology Letters,
32(4):312-316, 2002.
K. M. Furati
and M. A. El-Gebeily. A higher order method for nonlinear singular two-point
boundary valued problems. International
Journal of Mathematics and Mathematical Sciences,
30(5):257-269, 2002.
H. T. Banks,
D. G. Cole, K. M. Furati, K. Ito, and G. A. Pinter. A computational model
for sound field absorption by acoustic arrays.
Journal of Intelligent Material Systems and Structures,
13(4):231-240, 2002.
K. M. Furati. A
model for simulating frequency conversion in nonlinear optical media.
Journal of Computational Methods in Sciences and
Engineering, 3(1):99-107, 2003.
K. M. Furati
and M. A. El-Gebeily. Regular approximation of singular second order
differential expressions. Journal of
Mathematical Analysis and Applications,
283:100-113, 2003.
H. T. Banks,
K. M. Furati, K. Ito, N. S. Luke, and C. J. Smith. Acoustic attenuation
employing variable wall admittance. Lecture
Notes in Control and Information Sciences,
286:15-26, 2003.
M. A.
El-Gebeily and K. M. Furati. Real self-adjoint Sturm-Liouville problems.
Applicable Analysis,
83(4), 377-387 2004.
K.M. Furati,
Mokhtar Kirane, and N. e. Tatar. Existence and asymptotic behavior for a
convection problem. Nonlinear Analysis,
59(3):407-424, 2004.
K.M. Furati and
N. e. Tatar. An existence result for a nonlocal fractional differential
problem. Journal of Fractional Calculus,
26:43-51, 2004.
Khaled M.
Furati, Hattan Tawfiq, and Abul Hasan Siddiqi. Simulation and visualization
of safing sensor. American Journal of
Applied Sciences, 2(8):1261-1265, 2005.
K. M. Furati
and A. H. Siddiqi. Fast algorithms for the Bean critical-state model for
superconductivity. Numerical Functional
Analysis and Optimization, 26(2):177-192,
2005.
K. M. Furati
and A. H. Siddiqi. Parallel algorithms for quasi-variational inequality
arising in type-II superconductivity model.
Numerical Functional Analysis and Optimization,
26(2):193-204, 2005.
Khaled M.
Furati and Nasser eddine Tatar. Power-type estimates for a nonlinear
fractional differential equation. Nonlinear
Analysis, 62:1025 - 1036, 2005.
K. M. Furati
and N.-e. Tatar. Uniform boundedness and stability for a viscoelastic
problem. Applied Mathematics and Computation,
167:1211-1220, 2005.
K. M. Furati
and N.-e. Tatar. Behaviour of solutions for a weighted Cauchy-type
fractional differential problem. Journal of
Fractional Calculus, 28:23-42, 2005.
B. S. Attili,
K. M. Furati, and M. I. Syam. An Efficient Implicit Runge-Kutta Method for
Second Order Systems. Applied Mathematics
and Computation, 178(2):229-238, 2006.
K. M. Furati
and N. e. Tatar. Some fractional differential inequalities and their
applications. Mathematical Inequalities &
Applications, 9(4):577-598, 2006.
K. M.
Furati and N.-e. Tatar.
Long time behavior for a nonlinear fractional
model.
Journal of Mathematical Analysis and Applications,
332:441-454, 2007.
K. M. Furati
and M. Kirane. Necessary conditions for the existence of global solutions to
systems of fractional differential equations.
Fractional Calculus & Applied Analysis,
11(3):281-298, 2008.
M. A.
El-Gebeily, K. M. Furati, and Donal O'Regan. The finite element-Galerkin
method for singular self-adjoint differential equations.
Journal of Computational and Applied Mathematics,
223(2):735-752, January 2009.
M. A.
El-Gebeily, K. M. Furati, Donal O'Regan, and Ravi Agarwal. On the
approximation of nonlinear singular self-adjoint second order boundary value
problems. Journal of Computational and
Applied Mathematics, 224(1):360-372,
February 2009.
K. M. Furati
and N. e Tatar. Inequalities for fractional differential equations.
Mathematical Inequalities & Applications,
12(2):279-293, April 2009.
K. M. Furati. A fractional
differential inequality with application.
Nonlinear
Analysis TMA, 74(13):4330-4337, September
2011.
A. Al-Jaser and K. M. Furati,
Singular fractional integro-differential inequalities and applications,
Journal of Inequalities and Applications,
2011:110, 2011
K. M. Furati, M. D. Kassim and N.e-.
Tatar.
Existence and Uniqueness for a problem involving Hilfer
fractional derivative.
Computers and Mathematics with Applications,
64: 1616-1626, 2012.
K. M. Furati.
A Cauchy-type problem with a sequential
fractional derivative in the space of continuous functions.
Boundary Value Problem,
vol. 2012:58, 14 pages, 2012.
M. D. Qassim, K. M. Furati, and
N.-E. Tatar.
On a Differential Equation Involving
Hilfer-Hadamard Fractional Derivative, Abstract
and Applied Analysis, vol. 2012, Article ID
391062, 17 pages, 2012.
K. M. Furati,
Bounds on the solution of a Cauchy-type problem involving a weighted
sequential fractional derivative, Fractional
Calculus & Applied Analysis, 16(1):171-188,
2013.
A. Al-Jaser and K. M. Furati.
Inequalities for integro-differential equations
involving derivatives of order between zero and two,
Applied Mathematics and Computation,
221:535-546, 2013.
K. M. Furati.
A Cauchy-type problem involving a weighted
fractional derivative in the space of integrable functions.
Computers and Mathematics with Applications,
66:883-891, 2013.
Furati, K. M., M. Kassim, and N. M.
Tatar.
Non-existence of global solutions for a differential
equation involving Hilfer fractional derivative,
Electronic Journal of Differential Equations,
vol. 2013, no. 235, pp. 1-10, 2013.
Mustapha, K. A., B. S. Abdallah, and K. M. Furati, A
discontinuous Petrov-Galerkin method for time-fractional diffusion
equations, SIAM Journal on Numerical Analysis,
vol 52, no. 5, pp. 2512-2529, 2014.
Furati, K. M., O. S. Iyiola, and M. Kirane, An inverse
problem for a generalized fractional diffusion,
Applied Mathematics and Computation, vol 249,
pp. 24-31, 2014.
A. M. Khaliq, X. Liang, and K. M. Furati, "A
fourth-order implicit-explicit scheme for the space fractional nonlinear
Schrodinger equations," Numerical Algorithms,
vol. 75, pp. 147-172, 2017.
M. M. Ahmad, K. M. Furati, and N. M. Tatar,
"On the nonexistence of global solutions for a class of fractional
integro-differential problem," Advances in
Difference Equations, vol. 2017, pp. 59, 2017.
M. M. Ahmad, K. M. Furati, and N. M. Tatar,
"Asymptotic power type behavior of solutions to a nonlinear fractional
integro-differential equation," Electronic
Journal of Differential Equations, vol. 2017,
no. 134, pp. 1-16, 2017.
X. Liang, A. M. Khaliq, H. Bhatt, and K. M.
Furati, "The locally extrapolated exponential splitting scheme for
multi-dimensional nonlinear space-fractional Schrodinger equations," Numerical
Algorithms, vol. 76, pp. 939-958, 2017.
K. M. Furati, M. Yousuf, and A. Q. M. Khaliq,
"Fourth order methods for space fractional systems of reaction-diffusion
equations with nonsmooth data," International
Journal of Computer Mathematics, vol. 95, no.
6-7, pp. 1240-1256, 2018.
O. S. Iyiola, E. O. Asante-Asamani, K. M. Furati, A. Q.
M. Khaliq, and B. A. Wade, "Efficient time discretization scheme for
nonlinear space fractional reaction-diffusion equations," International
Journal of Computer Mathematics,
vol. 95, no. 6-7, pp. 1274-1291,
2018.
A. Q. M. Khaliq, T. A. Biala, S. S. Alzahrani, and K.
M. Furati, "Linearly implicit predictor-corrector methods for
space-fractional reaction-diffusion equations with non-smooth initial
data," Computers & Mathematics with Applications,
vol 75, 2629-2657, 2018.
Ahmad M.
Ahmad, Khaled M. Furati, Nasser-Eddine Tatar, “Boundedness and power-type
decay of solutions for a class of generalized fractional Langevin
equations,” Arabia Journal of Mathematics,
2018
Ahmad M. Ahmad, Khaled M. Furati, Nasser-Eddine
Tatar, “Asymptotic
Behavior of Solutions for a Class of Fractional Integro-differential
Equations,”
Mediterranean Journal of Mathematics, vol
15:188, 2018
Conference Papers
[1] K. Furati. The Riemann problem for polymer flooding with hysteresis. In J. Glimm, M. J. Graham, J. W. Grove, and B. J. Plohr, editors, Proceedings of the Fifth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Stony Brook, NY, 1994, pages 320-326. World Scientific, 1996.
[2] M. A. El-Gebeily and K. M. Furati, "A Shooting Method for Nonlinear Singular Boundary Value and Sturm-Liouville Problems," in Proceedings of the 16th IMACS World Congress, IMACS, Lausanne-Switzerland, 2000, pp. 21-25.
[3] G. Daspit, C. Martin, J-H. Pyo, C. Smith, H. To, K. M. Furati, Z. Ounaies, and R. C. Smith. Model development for piezoelectric polymer unimorphs. In Vittal S. Rao, editor, Smart Structures and Materials 2002: Modeling, Signal Processing, and Control, volume 4693 of Proceedings of SPIE, pages 514-524, 2002.
[4] K. M. Furati. A Cauchy-type problem involving a weighted sequential derivative. In 5th IFAC Symposium on Fractional Differentiation and its Applications (FDA12). Nanjing, China, May 2012.
Book Chapters
[1] K. M. Furati and A. H. Siddiqi. Mathematical models and algorithms for type-II superconductors. In Mathematical Models and Methods for Real World Systems, volume 272 of Pure and Applied Mathematics, pages 47-69, 2006.
[2] K. M. Furati, P. Manchanda, M. K. Ahmad, and A. H. Siddiqi. Trends in wavelet applications. In Mathematical Models Methods for Real World Systems, volume 272 of Pure and Applied Mathematics, pages 125-177, 2006.
[3] K. M. Furati and A. H. Siddiqi, "Wavelet Approximation of Safing Sensor Model," in Modern Mathematical Models, Methods and Algorithms for Real World Systems, A. H. Siddiqi, Iain S. Duff, and O. Christensen, Ed. New Delhi: Anamaya Publishers, 2007, pp. 60-79.
Books Editing
K. M. Furati, Z. Nashed, and A. H. Siddiqi. Mathematical Models and Methods for Real World Systems, volume 272 of Pure and Applied Mathematics. Chapman Hall/CRC, 2006.