Ph.D. in Applied Mathematics (Integral Equations and Elasticity)
Umm Al-Qura University: Makkah, SA
MScs. in Applied Mathematics (Integral Equations and Numerical Analysis)
Umm Al-Qura University: Makkah, SA
Bachelor's Degree in Mathematics
King Abdulaziz University: Jeddah, SA
RESEARCH INTERESTS
Integral equation, Elasticity, Numerical Analysis
10
Scopus Publications
75
Scholar Citations
5
Scholar h-index
2
Scholar i10-index
Scopus Publications
Phase-Lag Integro-Partial Differential Equation: Local and Nonlocal Solutions Sameeha Ali Raad Advances in Mathematical Physics, 2026 Nonlocal information, such as material deformation, genetic genes, or the history of the disease, are essential as they provide us with additional details that increase the numerical solution’s accuracy. With the help of the phase delay, we may also predict the future of the phenomena we are researching. This study involves consideration of both the nonlocal conditions and the phase delay effect. The phase‐lag integro‐partial differential equation (I‐PDE) with nonlocal conditions is investigated in order to achieve this, transforming it into a two‐dimensional mixed integral equation (2‐D MIE). The I‐PDE, thus, has a unique solution, as shown by the Banach fixed point theorem. Furthermore, the solution’s convergence has been demonstrated using Picard’s approach. Since the obtained MIE equation requires a specific approach to find its solution. In this investigation, MIE is numerically addressed using the product Nyström method (PNM). Ultimately, numerical results were obtained by solving various types of applications. Therefore, many interesting conclusions were derived.
A Suitable Algorithm to Solve a Nonlinear Fractional Integro-Differential Equation with Extended Singular Kernel in (2+1) Dimensions Sameeha Ali Raad, Mohamed Abdella Abdou Fractal and Fractional, 2025 In this paper, the authors consider a problem with comprehensive properties in terms of form and content in the space L2a,b×c,d×C0,T,T<1. In terms of time form, we assume that the time phase delay is implicitly contained in a nonlinear differential integral equation. The positional part is considered in two dimensions, and the position’s kernel is a general singular kernel, many different forms of which will be derived. In terms of content, all of the previously established numerical techniques are only appropriate for studying special cases of the kernel separately but are not suitable for studying the general kernel. This led to the use of the Toeplitz matrix method, which deals with the kernel in its extended nonlinear form and the special kernels will be studied as applications of the method. Moreover, this method has the advantage of converting all single integrals into regular integrals that can be easily solved. Additionally, the researchers examine the solution’s existence, uniqueness, and convergence in this paper. The error and its stability are also studied. At the end of the research, the authors studied some numerical applications of some of the singular kernels derived from the general kernel, examining the approximation error in each application separately.
The Effect of Fractional Order of Time Phase Delay via a Mixed Integral Equation in (2 + 1) Dimensions with an Extended Discontinuous Kernel Sameeha A. Raad, Mohammed A. Abdou Symmetry, 2025 It is common knowledge that studying integral equations accompanied by and related to phase delay is significant, and that significance grows when considering the problem’s time factor. Through this study, one may predict the material’s state for a short time or infer its state before beginning the investigation. In this work, a phase-lag mixed integral equation (P-MIE) with a continuous kernel in time and a singular kernel in position is studied in (2 + 1) dimensions in the space L2([a,b]×[c,d])×C[0,T],T<1. The properties of fractional integrals are used to generate the mixed integral equation (MIE). Certain assumptions are considered in order to examine convergence, uniqueness of solution, and estimation error. We achieve a class of two-dimensional Fredholm integral equations (FIEs) with time-dependent coefficients after applying the separation technique. After that, we will get a linear algebraic system (LAS) in 2Ds applying the product Nystrӧm method (PNM). The convergence of the LAS’s unique solution is covered. Two applications on the MIE with a logarithmic kernel and a Carleman function are discussed to illustrate the viability and efficiency of the applied techniques. At the end, a valuable conclusion is established.
Toeplitz Matrix Method and Nonlinear Volterra–Fredholm Integral Equation With Hilbert Kernel Sameeha Ali Raad, Ahlam Yahya Alabdali Computational and Mathematical Methods, 2025 This work emphasizes the investigation of the solution to the nonlinear Volterra–Fredholm integral equation (NV‐FIE) and the necessary conditions for a unique solution. The first step is to convert the NV‐FIE into a system of nonlinear Fredholm integral equations (NFIEs) using the splitting of the time interval. Analytical and semianalytical approaches are unable to solve this kind of singular integral equation due to the cumulative increase in error. While the Toeplitz matrix method (TMM) is considered one of the best methods to solve singular integral equations, its importance lies in the fact that it addresses singularity and provides simple, direct integrals. Therefore, in this study, the TMM is employed on the MIE to obtain an algebraic system. Finally, a numerical example is discussed as an application, and the error is calculated. One of the most prominent results of this study is the flexibility and efficiency of TMM in solving integral equations when the kernel takes the Hilbert type.
An Algorithm for the Solution of Integro-Fractional Differential Equations with a Generalized Symmetric Singular Kernel Sameeha A. Raad, Mohammed A. Abdou Fractal and Fractional, 2024 This work studies an integro-fractional differential equation (I-FrDE) with a generalized symmetric singular kernel. The scientific approach in this study was to transform the integro-differential equation (I-DE) into a mixed integral equation (MIE) with an Able kernel in fractional time and a generalized symmetric singular kernel in position. Additionally, the authors first set conditions on the singular kernels, whether related to time or position, and then transform the integral equation into an integral operator. Secondly, the solution is unique, which is proven by means of fixed-point theorems. In combination with the solution rules, the convergence of the solution is studied, and the error equation resulting from the solution is a stable error-integral influencer equation. Next, to solve this MIE, the authors apply a special technique to separate the variables and produce an integral equation in position with coefficients, in the form of an integral operator in time. As the most effective technique for resolving singular integral equations, the Toeplitz matrix method (TMM) is utilized to convert the integral equation into an algebraic system for the purpose of solving the position problem. The existence of a solution to the linear algebraic system in Banach space is then demonstrated. Lastly, certain applications where the functions of the generalized symmetric kernel are cubic or exponential and it assumes the logarithmic, Cauchy, or Carleman form are discussed. In each case, Maple 18 is also used to compute the error estimate.
Toeplitz matrix and Nyström method for solving linear fractional integro-differential equation Sameeha Raad, Khawlah AlQurashi European Journal of Pure and Applied Mathematics, 2022 In this paper, the Volterra-Fredholm integral equation is derived from a linear integro-differential equation with a fractional order 0 < α < 1 using Riemann–Liouville fractional integral. The existence and uniqueness of the solution are proved using the Picard method. Popular numerical methods; the Toeplitz matrix, and the product Nystr ̈om are used in the solution. These methods will prove their effective in solving this type of equation. Two examples are solved using the mentioned methods and the estimation error is calculated. Finally, a comparison between the numerical results is made.
New numerical approach for the nonlinear quadratic integral equations M. A Abdou, S. A Raad Journal of Computational and Theoretical Nanoscience, 2016 In this paper, the existence of a unique solution of the nonlinear quadratic integral equation (NQIE) of the second kind with continuous kernels, under certain conditions, is considered. Then, Adomian Decomposition Method (ADM) and new modifications have been considered to obtain a nonlinear algebraic system (NAS), where the existence of a unique solution of this method is also, proved. Finally, numerical results are computed when the continuous kernels take some different forms. Moreover, the rate of convergence error, in each case, is computed.
Fundamental contact problem and singular mixed integral equation Life Science Journal, 2014
Fundamental contact problem and singular mixed integral equation Life Science Journal, 2014
RECENT SCHOLAR PUBLICATIONS
A Suitable Algorithm to Solve a Nonlinear Fractional Integro-Differential Equation with Extended Singular Kernel in (2+ 1) Dimensions RS Ali, AM Abdella Fractal and Fractional 9 (4), 239 , 2025 2025 Citations: 3
The Effect of Fractional Order of Time Phase Delay via a Mixed Integral Equation in (2+ 1) Dimensions with an Extended Discontinuous Kernel SA Raad, MA Abdou Symmetry 17 (1), 36 , 2025 2025 Citations: 3
An Algorithm for the Solution of Integro-Fractional Differential Equations with a Generalized Symmetric Singular Kernel SA Raad, MA Abdou Fractal and Fractional 8 (11), 644 , 2024 2024 Citations: 6
Toeplitz matrix and Nyström method for solving linear fractional integro-differential equation S Raad, K Alqurashi European Journal of Pure and Applied Mathematics 15 (2), 796-809 , 2022 2022 Citations: 5
Nyström Method to Solve Two-Dimensional Volterra Integral Equation with Discontinuous Kernel SA Raad, MM Al-Atawi Journal of Computational and Theoretical Nanoscience 18 (4), 1177-1184 , 2021 2021 Citations: 3
A Numerical Treatment of Two-Dimensional Quadratic Volterra Integral Equation of the Second Kind SA Raad, MM Al-Atawi International Journal of Mathematics and Computer Applications Research 9 (2 … , 2019 2019
On Numerical Treatment for Volterra – Nonlinear Quadratic Integral Equation in Two-Dimensions SA Raad IOSR Journal of Mathematics (IOSR-JM) 13 (Issue 1 Ver. VI), 06-15 , 2017 2017
New numerical approach for the nonlinear quadratic integral equations MA Abdou, SA Raad Journal of Computational and Theoretical Nanoscience 13 (10), 6435-6439 , 2016 2016 Citations: 6
Nonlocal solution of a nonlinear partial differential equation and its equivalent of nonlinear integral equation MA Abdou, SA Raad Journal of Computational and Theoretical Nanoscience 13 (7), 4580-4587 , 2016 2016 Citations: 3
A New Numerical Treatment for the Nonlinear Quadratic Integral Equation in Two-Dimensions SA Raad Universal Journal of Integral Equations 4, 30-41 , 2016 2016 Citations: 2
Numerical Treatments to Solve the Two-dimensional Mixed Integral Equation in Time and Position SARSEAH M.A. Abdou, M.M. El-Kojok OJATM 2 (1), 40-54 , 2016 2016 Citations: 2
On Numerical Treatments to Solve a Volterra–Hammerstein Integral Equation SA Raad BJMCS 14 (6), 1-15 , 2016 2016 Citations: 2
On a Discussion of Fredholm – Urysohn integral equation with singular kernel in time MMEKSA Raad Universal Journal of Integral Equations 3, 51-60 , 2015 2015
Non-Local solution of mixed integral equation with singular kernel MA Abdou, SA Raad, W Wahied Glob. J. Sci. Front. Res. Math. Decis. Sci 15, 1-13 , 2015 2015 Citations: 4
Mixed Integral Equations and Contact Problems S Raad, MAA Abdou LAP LAMBERT Academic Publishing , 2014 2014
Analytic and Numeric Solution of Nonlinear Partial Differential Equations of Fractional Order SAR M. A. Abdou, M. M. El–kojok International journal of pure mathematics 1, 47-55 , 2014 2014
On the solution of Fredholm-Volterra integral equation with discontinuous kernel in time MA Abdou, MM El-Kojok, SA Raad Journal: JOURNAL OF ADVANCES IN MATHEMATICS 9 (4) , 2014 2014 Citations: 3
Fundamental contact problem and singular mixed integral equation MA Abdou, S Raad, S Al-Hazmi Life Sci. J. 8, 323-329 , 2014 2014 Citations: 15
Analytic and Numeric Solution of Linear Partial Differential Equation of Fractional Order MA Abdou, MK El-Kojak, SA Raad Global Journal of Science Frontier Research Mathematics and Decision … , 2013 2013 Citations: 12
Mixed integral equation in position and time with weakly kernels SAR M. A. Abdou International Journal of Applied Mathematics and Computation 2 (2), 57-67 , 2010 2010 Citations: 3
MOST CITED SCHOLAR PUBLICATIONS
Fundamental contact problem and singular mixed integral equation MA Abdou, S Raad, S Al-Hazmi Life Sci. J. 8, 323-329 , 2014 2014 Citations: 15
Analytic and Numeric Solution of Linear Partial Differential Equation of Fractional Order MA Abdou, MK El-Kojak, SA Raad Global Journal of Science Frontier Research Mathematics and Decision … , 2013 2013 Citations: 12
An Algorithm for the Solution of Integro-Fractional Differential Equations with a Generalized Symmetric Singular Kernel SA Raad, MA Abdou Fractal and Fractional 8 (11), 644 , 2024 2024 Citations: 6
New numerical approach for the nonlinear quadratic integral equations MA Abdou, SA Raad Journal of Computational and Theoretical Nanoscience 13 (10), 6435-6439 , 2016 2016 Citations: 6
Toeplitz matrix and Nyström method for solving linear fractional integro-differential equation S Raad, K Alqurashi European Journal of Pure and Applied Mathematics 15 (2), 796-809 , 2022 2022 Citations: 5
Non-Local solution of mixed integral equation with singular kernel MA Abdou, SA Raad, W Wahied Glob. J. Sci. Front. Res. Math. Decis. Sci 15, 1-13 , 2015 2015 Citations: 4
A Suitable Algorithm to Solve a Nonlinear Fractional Integro-Differential Equation with Extended Singular Kernel in (2+ 1) Dimensions RS Ali, AM Abdella Fractal and Fractional 9 (4), 239 , 2025 2025 Citations: 3
The Effect of Fractional Order of Time Phase Delay via a Mixed Integral Equation in (2+ 1) Dimensions with an Extended Discontinuous Kernel SA Raad, MA Abdou Symmetry 17 (1), 36 , 2025 2025 Citations: 3
Nyström Method to Solve Two-Dimensional Volterra Integral Equation with Discontinuous Kernel SA Raad, MM Al-Atawi Journal of Computational and Theoretical Nanoscience 18 (4), 1177-1184 , 2021 2021 Citations: 3
Nonlocal solution of a nonlinear partial differential equation and its equivalent of nonlinear integral equation MA Abdou, SA Raad Journal of Computational and Theoretical Nanoscience 13 (7), 4580-4587 , 2016 2016 Citations: 3
On the solution of Fredholm-Volterra integral equation with discontinuous kernel in time MA Abdou, MM El-Kojok, SA Raad Journal: JOURNAL OF ADVANCES IN MATHEMATICS 9 (4) , 2014 2014 Citations: 3
Mixed integral equation in position and time with weakly kernels SAR M. A. Abdou International Journal of Applied Mathematics and Computation 2 (2), 57-67 , 2010 2010 Citations: 3
Fredholm–Volterra integral equations with logarithmic kernel M Abdou, S Raad J. Appl. Math. Comput 176, 215-224 , 2006 2006 Citations: 3
A New Numerical Treatment for the Nonlinear Quadratic Integral Equation in Two-Dimensions SA Raad Universal Journal of Integral Equations 4, 30-41 , 2016 2016 Citations: 2
Numerical Treatments to Solve the Two-dimensional Mixed Integral Equation in Time and Position SARSEAH M.A. Abdou, M.M. El-Kojok OJATM 2 (1), 40-54 , 2016 2016 Citations: 2
On Numerical Treatments to Solve a Volterra–Hammerstein Integral Equation SA Raad BJMCS 14 (6), 1-15 , 2016 2016 Citations: 2
A Numerical Treatment of Two-Dimensional Quadratic Volterra Integral Equation of the Second Kind SA Raad, MM Al-Atawi International Journal of Mathematics and Computer Applications Research 9 (2 … , 2019 2019
On Numerical Treatment for Volterra – Nonlinear Quadratic Integral Equation in Two-Dimensions SA Raad IOSR Journal of Mathematics (IOSR-JM) 13 (Issue 1 Ver. VI), 06-15 , 2017 2017
On a Discussion of Fredholm – Urysohn integral equation with singular kernel in time MMEKSA Raad Universal Journal of Integral Equations 3, 51-60 , 2015 2015
Mixed Integral Equations and Contact Problems S Raad, MAA Abdou LAP LAMBERT Academic Publishing , 2014 2014
