Summary
I am Dr. Umer Saeed, currently serving as an Associate Professor of Mathematics at the National University of Sciences and Technology (NUST), Pakistan. I have over a decade of teaching and research experience in applied and computational mathematics. I completed my Postdoctoral Research Fellowship (Feb 2024 – Jan 2025) at the Ulsan National Institute of Science and Technology (UNIST), South Korea, under the supervision of Professor Bongsoo Jang, where my research focused on hybrid wavelet methods and fractional differential equations. I have been actively engaged in teaching undergraduate and postgraduate courses such as Differential Equations, Linear Algebra, Numerical Methods, and Probability and Statistics. My teaching philosophy emphasizes conceptual understanding, analytical reasoning, and the integration of computational tools such as MATLAB to bridge theory and practical applications. My primary research interests include wavelet analysis, fractional calculus, numerical methods, bifurcation analysis, and mathematical biology. Over the years, I have developed several efficient and accurate numerical techniques for solving nonlinear and fractional-order differential equations. I have published more than 50 research papers in reputable international journals, including Applied Mathematics and Computation, Nonlinear Dynamics, Mathematical Methods in the Applied Sciences, Mathematical Sciences, Engineering Computations, Advances in Difference Equations, Zeitschrift für Naturforschung A, and Journal of Vibration and Control. In addition to research, I have supervised multiple MS and PhD students, contributing to the development of emerging researchers in applied mathematics. I also serve as a reviewer for several high-impact international journals. My academic journey reflects a strong commitment to both teaching and research excellence, advancing the fields of fractional calculus, wavelet methods, and their applications in science and engineering.
Academic Background
PhD
(Mathematics) NUST, Islamabad
September 01, 2009 - February 16, 2015
Honours and Awards
Publications
A new method for nonlinear Katugampola fractional differential equations
June 30, 2026
Mathematical Sciences - Volume 20(2), Pages 145-157
Fast shifted Legendre wavelets method for solving two-dimensional nonlinear fractional partial differential equations
January 16, 2026
Computational and Applied Mathematics - Volume 45, Article Number 211
A new method for one and higher dimensional linear and nonlinear tempered Caputo fractional diffusion-type equations
December 25, 2025
Engineering Computations - Volume 42, Issue:10, Pages:28
Analyzing Dynamics, Bifurcations, and Chaos in a Discrete Predator-Prey System with Ricker Growth: A Theoretical and Empirical Investigation
December 06, 2025
Mathematical Methods in the Applied Sciences - Pages 1-42
Hybrid Wavelet Methods for Nonlinear Multi-Term Caputo Variable-Order Partial Differential Equations
August 31, 2025
CMES-Computer Modeling in Engineering & Sciences - Volume 144(2), Pages 2165-2189
Modified Haar wavelet method for linear and nonlinear Caputo fractional variable-order diffusion type equations
August 05, 2025
Engineering Computations - Pages:21
Efficient Algorithms for the Solution of Linear and Nonlinear Caputo-Tempered Variable Order Partial Differential Equations
June 30, 2025
Mathematical Sciences - Volume 19(2), Pages 1-19
A generalized fractional-order discrete Hahn wavelet method for solving nonlinear fractional differential equations
May 20, 2025
Engineering Computations - Volume 42 No. 5, Pages 1728-1750
A new scheme for the solution of the nonlinear Caputo–Hadamard fractional differential equations
October 01, 2024
Alexandria Engineering Journal - Volume: 105, Pages 56-69
A method for solving Caputo–Hadamard fractional initial and boundary value problems
September 15, 2023
Mathematical Methods in the Applied Sciences - Volume 46, Issue13, Pages 13907-13921
A generalized CAS wavelet method for solving ψ-Caputo fractional differential equations
August 15, 2023
Engineering Computations - Volume 40, Issue 06, Pages 1351-1370
Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System
February 20, 2023
Match - Volume 90, Issue 1, Pages 151-174
Modification of Nicholson–Bailey model under refuge effects with stability, bifurcation, and chaos control
December 01, 2022
Journal of Vibration and Control - Volume 28, Issue (23-24), Pages 3524-3538
Krawtchouk wavelets method for solving Caputo and Caputo–Hadamard fractional differential equations
November 30, 2022
Mathematical Methods in the Applied Sciences - Volume 45, Issue 17, Pages 11331-11354
Vieta–Lucas wavelets method for fractional linear and nonlinear delay differential equations
November 15, 2022
Engineering Computations - Volume 39, Issue 9, Pages 3211-3231
Generalized sine–cosine wavelet method for Caputo–Hadamard fractional differential equations
November 15, 2022
Mathematical Methods in the Applied Sciences - Volume 45, Issue 16, Pages 9602-9621
A generalized Taylor operational matrix method for ψ-fractional differential equations
October 17, 2022
Mathematical Methods in the Applied Sciences - Pages 1-23
Porosity effects on the peristaltic flow of biological fluid in a complex wavy channel
March 01, 2022
Pramana - Journal of Physics - Volume 96, Article Number: 2
A wavelet method for solving Caputo–Hadamard fractional differential equation
February 08, 2022
Engineering Computations - Volume 39, No. 2, Pages 650-671
Fractional Gegenbauer wavelets operational matrix method for solving nonlinear fractional differential equations
February 04, 2021
Mathematical Sciences - Pages 1-15
Green–Haar wavelets method for generalized fractional differential equations
September 22, 2020
Advances in Difference Equations - Volume 2020, Article Number: 515
ψ-Haar wavelets method for numerically solving fractional differential equations
August 12, 2020
Engineering Computations - Volume 38, Issue 2, Pages 1037-1056
2D numerical modeling of two dam-break flood model studies in an urban locality
July 17, 2020
Arabian Journal of Geosciences - Volume 13, Article Number 682
Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation
July 08, 2020
Journal of Mathematics - Volume 2020, Article ID 6737098, 13 pages
Green-Haar method for fractional partial differential equations
April 16, 2020
Engineering Computations - Volume 37, Issue 4, Pages 1473-1490
Bifurcation analysis and chaos control in discrete-time modified Leslie–Gower prey harvesting model
January 21, 2020
Advances in Difference Equations - Volume 2020, Article Number 45
Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method
December 02, 2019
Mathematics - Vol.7(12), Article Number 1164
Sine‐cosine wavelet method for fractional oscillator equations
December 01, 2019
Mathematical Methods in the Applied Sciences - Volume 42, Issue18, Pages 6960-6971
Peristaltic transportation of fluid through simple and complex wavy nonuniform channels: A bioengineering application
December 01, 2019
International Journal for Multiscale Computational Engineering - Volume 17, Issue 6, Pages 623-638
Bifurcation analysis and chaos control in a discrete-time plant quality and larch budmoth interaction model with Ricker equation
November 19, 2019
Mathematical Methods in the Applied Sciences - Volume 42, Issue 18, Pages 7395-7410
A modified method for solving non-linear time and space fractional partial differential equations
August 12, 2019
Engineering Computations - Volume 36, Issue 7, Pages 2162-2178
Generalized fractional order Chebyshev wavelets for solving nonlinear fractional delay-type equations
May 01, 2019
International Journal of Wavelets, Multiresolution and Information Processing - Volume 17, Issue 3, Article Number 1950014
Sine–cosine wavelets operational matrix method for fractional nonlinear differential equation
April 09, 2019
International Journal of Wavelets, Multiresolution and Information Processing - Volume 17, Issue No. 04, Article 1950026
Bifurcation analysis and chaos control in discrete-time system of three competing species
March 01, 2019
Arabian Journal of Mathematics - Volume 8, Issue 1, Pages 1-14
Differential quadrature method for nonlinear fractional partial differential equations
October 17, 2018
Engineering Computations - Volume 35, Issue 6, Pages 2349-2366
CAS Wavelet Picard Technique for Burger?s?Huxley and Burgers Equation
October 01, 2018
International journal of applied and Computational Mathematics - NULL
Neimark?Sacker bifurcation and chaos control in discrete-time predator?prey model with parasites
August 12, 2018
Nonlinear Dynamics - Pages 1–10
CAS wavelet quasi-linearization technique for the generalized Burger?Fisher equation
March 01, 2018
Mathematical Sciences - NULL
Haar Adomian Method for the Solution of Fractional Nonlinear Lane-Emden Type Equations Arising in Astrophysics
October 01, 2017
TAIWANESE JOURNAL OF MATHEMATICS - NULL
Bifurcation analysis and chaos control in a host-parasitoid model
September 30, 2017
Mathematical Methods in the Applied Sciences - Volume 40, Issue 14, Pages 5391-5406
Haar wavelet operational matrix method for system of fractional nonlinear differential equations
September 15, 2017
International Journal of Wavelets, Multiresolution and Information Processing - Volume 15, Issue 5, Article Number 1750043
CAS Picard method for fractional nonlinear differential equation
August 15, 2017
Applied Mathematics and Computation - Volume: 307, Pages: 102-112
A quadrature method for numerical solutions of fractional differential equations
August 15, 2017
Applied Mathematics and Computation - Volume 307, Pages 38-49
Fractional-Order Vector-Host Disease Model
April 01, 2017
Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms - Volume 24, Pages 97-111
Radial basis function networks for delay differential equation
September 01, 2016
Arabian Journal of Mathematics - Volume 5, Pages 139-144
Modified Variational Iteration Method for Sine-Gordon Equation
August 01, 2016
TEM Journal - Volume 5, Issue 3, Pages 305-312
Qualitative behavior of a smoking model
April 05, 2016
Advances in Difference Equations - Volume:2016, Issue:1, Article Number:96
Qualitative Behaviour of Generalised Beddington Model
February 01, 2016
Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences - Volume 71, Issue 2, Pages 145-155
Gegenbauer wavelets operational matrix method for fractional differential equations
September 01, 2015
Journal of the Korean Mathematical Society - Volume: 52, Issue: 5, Pages: 1069-1096
Modified Chebyshev wavelet methods for fractional delay-type equations
August 01, 2015
Applied Mathematics and Computation - Volume 264, Pages 431-442
Haar wavelet Picard method for fractional nonlinear partial differential equations
August 01, 2015
Applied Mathematics and Computation - Volume: 264, Pages: 310-322
Modified Laguerre Wavelets Method for delay differential equations of fractional-order
March 01, 2015
Egyptian Journal of Basic and Applied Sciences - Volume 2, Issue 1, Pages 50-54
Haar wavelet operational matrix method for fractional oscillation equations
July 15, 2014
International Journal of Mathematics and Mathematical Sciences - Volume 2014, Article ID 174819, 8 pages
Hermite Wavelet Method for Fractional Delay Differential Equations
July 02, 2014
Journal of Difference Equations - Volume 2014, Article ID: 359093
Haar Wavelet-Picard technique for fractional order nonlinear initial and boundary value problems
June 30, 2014
Scientific Research and Essays - Volume 9(12), Pages 571-580
Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems
June 16, 2014
Abstract and Applied Analysis - Volume 2014, Article ID 868934, 10 pages
Assessment of Haar wavelet-quasilinearization technique in heat convection-radiation equations
February 05, 2014
Applied Computational Intelligence and Soft Computing - Volume 2014, Article ID 454231, 5 Pages
Fractional order SEIRS model
January 01, 2014
Advanced Studies in Biology - Volume 6, No. 2, Pages 47-56
Haar wavelet-quasilinearization technique for fractional nonlinear differential equations
September 01, 2013
Applied Mathematics and Computation - Volume: 220, Pages: 630-648
Conferences
Hybrid Wavelet Methods for Nonlinear Multi-Term Caputo Variable-Order Partial Differential Equations
December 05, 2024 - December 08, 2024
Umer Saeed, Junseo Lee, Bongsoo Jang,
KSIAM
A method for solving nonlinear fractional partial differential equations
February 20, 2019 - February 22, 2019
Umer Saeed,
International Conference of Recent Advances in Applied Mathematics
Wavelet method for the solution of nonlinear partial differential equations
November 07, 2017 - November 08, 2017
Umer Saeed,
NUST Conference on Recent Trends in Mathematical Sciences
A Method for the Solution of Generalized Burger-Fisher Equation
April 08, 2017 - April 09, 2017
Umer Saeed,
Recent Advances in Mathematical Methods, Models and Applications (RAMMMA17)
CAS Quasilinearization Technique for the Solution of the Nonlinear Lane-Emden Type Equations Arising in Astrophysics
April 09, 2016 - April 10, 2016
Umer Saeed,
Conference on Recent Advances in Mathematical Methods, Models & Applications
Assistant Professor
The University of Poonch Rawalakot
May 13, 2015 - September 03, 2015