About
Professional SummaryProf. Omar Abu Arqub received his Ph.D. degree in the Applied Mathematics from the University of Jordan in 2009. His research interests focus on the following subjects: Numerical Analysis, Computational Optimization, Inverse Problems, Differential Inequalities, Fractional Calculus Theory, Fuzzy Calculus Theory, Stochastic Calculus Theory, Optimal Control Theory, Signal Processing Theory.
Education
Academic Background-
Ph.D. The University of Jordan, Jordan Applied Mathematics | Completed: 2008
-
M.Sc. The University of Jordan, Jordan Applied Mathematics | Completed: 2002
-
B.Sc. Mutah University, Alkarak, Jordan Applied Mathematics | Completed: 1996
Publications (117)
Selected Scholarly Contributions
Convergence analysis and analytical approximation of fractional modified Camassa–Holm and Degasperis–Procesi equations via a hybrid transform–iterative framework
2026
New classes of wave solutions for nonlinear conformable space-time PDEs via the Riccati sub-equation approach: analysis of the Bateman-Burgers, Clannish Random Walker's parabolic, and Estevez-Mansfield-Clarkson equations
2026
Fractional analysis of time-fractional Emden–Fowler model arising in fluid flow of porous media and physical sciences
2026
AN INVERSE TIME-DEPENDENT DIFFUSION COEFFICIENT PROBLEM FOR A SPACE-FRACTIONAL DIFFUSION EQUATION
2026
THEORETICAL PREDICTIONS OF EXISTENCE AND UNIQUENESS FOR STOCHASTIC M-FRACTIONAL DIFFERENTIAL MODELS OF RANDOM BROWNIAN MOTION, EXHIBITED WITH MATRIX SPECTRAL COLLOCATION SOLUTIONS AND SIMULATED WITH THE ELECTRICAL ENGINEERING RLC UTILITY AS A CASE INTERPRETATION
2026
PREFACE: SPECIAL ISSUE ON “RECENT APPLICATIONS OF FRACTAL THEORY AND FRACTIONAL CALCULUS IN MATHEMATICAL PHYSICS”
2026
A stable regularization approach for reconstructing the initial displacement or the initial velocity in the fractional two-dimensional diffusion-wave equation
2026
Numerical Analysis Employing Matrix Spectral Collocation Step Method for Stochastic Conformable Differential Problems Stimulated by One-Dimensional Brownian Motion with Constant Discrete Delays
2026
Fractional Hilfer Lane-Emden type model arising in astrophysics: theoretical framework for existence and uniqueness assessment and numerical simulation using Lucas-base polynomials approach within the Galerkin residual strategy
2026
Delay volterra integrodifferential models of fractional orders and exponential kernels: Well-posedness theoretical results and Legendre–Galerkin shifted approximations
2025
Investigating the invariant solutions of (1+1)-dimensional Sawada–Kotera model using Lie symmetries analysis
2025
ANALYSIS AND COLLOCATION APPROXIMATIONS USING SHIFTED LEGENDRE GALERKIN ALGORITHM FOR SYSTEMS OF FRACTIONAL INTEGRODIFFERENTIAL DELAY PROBLEMS REGARDING HILFER FRACTIONAL TYPE
2025
THE PROSPECTIVE ANALYSIS OF THREE-DIMENSIONAL TIME-FRACTIONAL HELMHOLTZ MODEL USING A NEW ITERATIVE METHOD
2025
Soliton solutions and stability analysis to the Hirota-bilinear-like model using the unified Riccati equation expansion approach
2025
Bifurcation, chaos, and time series analysis of the Manakov model utilizing the unified Riccati equation expansion technique
2025
Theoretical study and numerical analysis using step spectral collocation method for stochastic M-fractional differential models of simplified Brownian motion within constant delays process
2025
Existence, uniqueness, and numerical analysis of fractional M-derivative stochastic integrodifferential models within the shifted Legendre Gauss pseudospectral algorithm
2025
Study of soliton solutions, bifurcation, and sensitivity analysis in the Davey–Stewartson–Kadomtsev–Petviashvili model
2025
Numerical analysis of Lucas polynomials innovative technique within the Galerkin strategy for solving fuzzy-type differential models with an application in the electrical circuit engineering field
2025
New analytical and approximate solutions for the time-conformable fractional Kersten–Krasil’shchik coupled KdV–mKdV nonlinear system
2025
Numerical Hilbert space solution of fractional Sobolev equation in $$\left(1+1\right)$$-dimensional space
2024
Uncertain M-fractional differential problems: existence, uniqueness, and approximations using Hilbert reproducing technique provisioner with the case application: series resistor-inductor circuit
2024
Existence, uniqueness, and galerkin shifted Legendre's approximation of time delays integrodifferential models by adapting the Hilfer fractional attitude
2024
The computational orthogonal shifted Legendre–Galerkin approach for handling fractional delay differential problems via adapting fractional M-derivative
2024
Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer (α,β)-framework set
2024
Existence, uniqueness, and collocation solutions using the shifted Legendre spectral method for the Hilfer fractional stochastic integro-differential equations regarding stochastic Brownian motion
2024
Bifurcation, chaotic analysis and soliton solutions to the (3+1)-dimensional p-type model
2024
Adaptation of kernel functions‐based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations
2023
Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator
2023
Adaptive the Dirichlet model of mobile/immobile advection/dispersion in a time-fractional sense with the reproducing kernel computational approach: Formulations and approximations
2023
Lie analysis and laws of conservation for the two-dimensional model of Newell–Whitehead–Segel regarding the Riemann operator fractional scheme in a time-independent variable
2023
Exploring the Analytical Solutions to the Economical Model via Three Different Methods
2023
Adaptation of the Novel Cubic B-Spline Algorithm for Dealing with Conformable Systems of Differential Boundary Value Problems concerning Two Points and Two Fractional Parameters
2023
Stochastic integrodifferential models of fractional orders and Leffler nonsingular kernels: well-posedness theoretical results and Legendre Gauss spectral collocation approximations
2023
Hilbert approximate solutions and fractional geometric behaviors of a dynamical fractional model of social media addiction affirmed by the fractional Caputo differential operator
2023
Analysis of Lie Symmetry, Explicit Series Solutions, and Conservation Laws for the Nonlinear Time-Fractional Phi-Four Equation in Two-Dimensional Space
2022
On the Recovery of a Conformable Time-Dependent Inverse Coefficient Problem for Diffusion Equation of Periodic Constraints Type and Integral Over-Posed Data
2022
Fractional Conformable Stochastic Integrodifferential Equations: Existence, Uniqueness, and Numerical Simulations Utilizing the Shifted Legendre Spectral Collocation Algorithm
2022
Lie symmetry analysis, explicit solutions, and conservation laws of the time-fractional Fisher equation in two-dimensional space.
Omar Abed Elkareem Abu Arqub
2022
Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the Atangana-Baleanu-Caputo derivative and the reproducing kernel scheme.
Omar Abed Elkareem Abu Arqub
2022
The cubic B-spline interpolation method for numerical point solutions of conformable boundary value problems.
Omar Abed Elkareem Abu Arqub
2022
The B-spline collocation method for solving conformable initial value problems of non-singular and singular types.
Omar Abed Elkareem Abu Arqub
2022
Development of the reproducing kernel Hilbert space algorithm for numerical pointwise solution of the time-fractional nonlocal reaction-diffusion equation.
Omar Abed Elkareem Abu Arqub
2022
A numerical method for solving conformable fractional integrodifferential systems of second-order, two-points periodic boundary conditions.
Omar Abed Elkareem Abu Arqub
2022
A novel analytical algorithm for generalized fifth-order time-fractional nonlinear evolution equations with conformable time derivative arising in shallow water waves.
Omar Abed Elkareem Abu Arqub
2022
The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique
2021
Reproducing kernel Hilbert pointwise numerical solvability of fractional Sine-Gordon model in time-dependent variable with Dirichlet condition
2021
A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations
2021
A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation
2021
Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis.
Omar Abed Elkareem Abu Arqub
2021
Numerical simulation of telegraph and Cattaneo fractional‐type models using adaptive reproducing kernel framework.
Omar Abed Elkareem Abu Arqub
2021
Residual Series Representation Algorithm for Solving Fuzzy Duffing Oscillator Equations
2020
A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method
2020
Numerical computations of coupled fractional resonant Schrödinger equations arising in quantum mechanics under conformable fractional derivative sense
2020
An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative
2020
Approximate solutions of nonlinear fractional Kundu-Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method
2020
Numerical solutions of riesz fractional diffusion and advection-dispersion equations in porous media using iterative reproducing kernel algorithm.
Omar Abed Elkareem Abu Arqub
2020
Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions.
Omar Abed Elkareem Abu Arqub
2020
Soliton solutions of a nonlinear fractional sasa-satsuma equation in monomode optical fibers.
Omar Abed Elkareem Abu Arqub
2020
An attractive analytic-numeric approach for the solutions of uncertain riccati differential equations using residual power series.
Omar Abed Elkareem Abu Arqub
2020
Solving space-fractional Cauchy problem by modified finite-difference discretization scheme.
Omar Abed Elkareem Abu Arqub
2020
Fitted spectral tau jacobi technique for solving certain classes of fractional differential equations.
Omar Abed Elkareem Abu Arqub
2020
Computing bifurcations behavior of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types in hilbert space with error analysis.
Omar Abed Elkareem Abu Arqub
2020
Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations.
Omar Abed Elkareem Abu Arqub
2019
Analytical solutions of fuzzy fractional boundary value problem of order 2α by using RKHS algorithm.
Omar Abed Elkareem Abu Arqub
2019
Modulation of reproducing kernel hilbert space method for numerical solutions of riccati and bernoulli equations in the atangana-baleanu fractional sense.
Omar Abed Elkareem Abu Arqub
2019
Application of residual power series method for the solution of time-fractional schrödinger equations in one-dimensional space.
Omar Abed Elkareem Abu Arqub
2019
Application of reproducing kernel algorithm for solving dirichlet time-fractional diffusion-gordon types equations in porous media.
Omar Abed Elkareem Abu Arqub
2019
Numerical algorithm for the solutions of fractional order systems of dirichlet function types with comparative analysis.
Omar Abed Elkareem Abu Arqub
2019
2018
Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm
2018
Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates.
Omar Abed Elkareem Abu Arqub
2018
Numerical solutions of integrodifferential equations of fredholm operator type in the sense of the atangana–baleanu fractional operator.
Omar Abed Elkareem Abu Arqub
2018
Modeling and analyzing neural networks using reproducing kernel hilbert space algorithm.
Omar Abed Elkareem Abu Arqub
2018
Atangana–Baleanu fractional approach to the solutions of Bagley–Torvik and Painlevé equations in Hilbert space.
Omar Abed Elkareem Abu Arqub
2018
Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates.
Omar Abed Elkareem Abu Arqub
2018
Computational algorithm for solving singular Fredholm time-fractional partial integrodifferential equations with error estimates.
Omar Abed Elkareem Abu Arqub
2018
Numerical solutions for the robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm.
Omar Abed Elkareem Abu Arqub
2018
Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space.
Omar Abed Elkareem Abu Arqub
2017
Numerical algorithm for solving time-fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions.
Omar Abed Elkareem Abu Arqub
2017
A novel iterative numerical algorithm for the solutions of systems of fuzzy initial value problems.
Omar Abed Elkareem Abu Arqub
2017
Bifurcations of the time-fractional generalized coupled Hirota-Satsuma KdV system.
Omar Abed Elkareem Abu Arqub
2017
A novel iterative numerical algorithm for the solutions of systems of fuzzy initial value problems.
Omar Abed Elkareem Abu Arqub
2017
Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions.
Omar Abed Elkareem Abu Arqub
2017
An efficient analytical method for solving singular initial value problems of nonlinear systems.
Omar Abed Elkareem Abu Arqub
2016
A residual power series technique for solving systems of initial value problems.
Omar Abed Elkareem Abu Arqub
2016
Analytical approximations of partial differential equations of fractional order with multistep approach.
Omar Abed Elkareem Abu Arqub
2016
Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems.
Omar Abed Elkareem Abu Arqub
2016
Solutions of Bagley-Torvik and painleve equations of fractional order using iterative reproducing kernel algorithm.
Omar Abed Elkareem Abu Arqub
2016
Approximate solutions of DASs with nonclassical boundary conditions using novel reproducing kernel algorithm.
Omar Abed Elkareem Abu Arqub
2016
Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method.
Omar Abed Elkareem Abu Arqub
2016
The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations.
Omar Abed Elkareem Abu Arqub
2016
Analytical simulation of singular second-order, three points BVPs for Fredholm operator using computational kernel algorithm.
Omar Abed Elkareem Abu Arqub
2016
An efficient computational method for handling singular second-order, three points Volterra integrodifferenital equations.
Omar Abed Elkareem Abu Arqub
2016
Numerical solutions of fuzzy differential equations using reproducing kernel hilbert space method.
Omar Abed Elkareem Abu Arqub
2016
Existence, uniqueness, and characterization theorems for nonlinear fuzzy integrodifferential equations of volterra type.
Omar Abed Elkareem Abu Arqub
2015
Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations.
Omar Abed Elkareem Abu Arqub
2015
A general form of the generalized Taylor`s formula with some applications.
Omar Abed Elkareem Abu Arqub
2015
A novel expansion iterative method for solving linear partial differential equations of fractional order.
Omar Abed Elkareem Abu Arqub
2015
Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations.
Omar Abed Elkareem Abu Arqub
2015
Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: A new iterative algorithm.
Omar Abed Elkareem Abu Arqub
2015
An optimization algorithm for solving systems of singular boundary value problems.
Omar Abed Elkareem Abu Arqub
2014
Application of continuous genetic algorithm for nonlinear system of second-order boundary value problems.
Omar Abed Elkareem Abu Arqub
2014
A novel multistep generalized differential transform method for solving fractional-order lu chaotic and hyperchaotic systems.
Omar Abed Elkareem Abu Arqub
2014
An iterative method for solving fourth-order boundary value problems of mixed type integro-differential equations.
Omar Abed Elkareem Abu Arqub
2014
Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations.
Omar Abed Elkareem Abu Arqub
2014
A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm-Voltera type.
Omar Abed Elkareem Abu Arqub
2014
Multiple solutions of nonlinear boundary value problems of fractional Order: A new analytic iterative technique.
Omar Abed Elkareem Abu Arqub
2014
Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm.
Omar Abed Elkareem Abu Arqub
2014
Application of continuous genetic algorithm for nonlinear system of second-order boundary value problems.
Omar Abed Elkareem Abu Arqub
2014
A Computational Method for Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential Equations
2013
2013
Analytical solutions of fuzzy initial value problems by ham.
Omar Abed Elkareem Abu Arqub
2013
Analytical solution of nonlinear second-order periodic boundary value problem using reproducing kernel method.
Omar Abed Elkareem Abu Arqub
2013
New results on fractional power Series: Theories and applications.
Omar Abed Elkareem Abu Arqub
2013
Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method.
Omar Abed Elkareem Abu Arqub
2013
Analytical solutions of fuzzy initial value problems by HAM.
Omar Abed Elkareem Abu Arqub
2013