Sameeha Raad

@uqu.edu.sa

Department of Mathematical Sciences
Umm Al-Qura University



                 

https://researchid.co/sameeharaad

EDUCATION

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

7

Scopus Publications

61

Scholar Citations

4

Scholar h-index

2

Scholar i10-index

Scopus Publications

  • 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 and Mohammed A. Abdou
    MDPI AG
    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.

  • An Algorithm for the Solution of Integro-Fractional Differential Equations with a Generalized Symmetric Singular Kernel
    Sameeha A. Raad and Mohammed A. Abdou
    MDPI AG
    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 and Khawlah AlQurashi
    New York Business Global LLC
    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 and S. A Raad
    American Scientific Publishers
    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


  • Fundamental contact problem and singular mixed integral equation


RECENT SCHOLAR PUBLICATIONS

  • Toeplitz matrix and Nystrm method for solving linear fractional integro-differential equation
    S Raad, K Alqurashi
    European Journal of Pure and Applied Mathematics 15 (2), 796-809 2022

  • Nystrm 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

  • 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

  • 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

  • New numerical approach for the nonlinear quadratic integral equations
    MA Abdou, SA Raad
    Journal of Computational and Theoretical Nanoscience 13 (10), 6435-6439 2016

  • 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

  • A New Numerical Treatment for the Nonlinear Quadratic Integral Equation in Two-Dimensions
    SA Raad
    Universal Journal of Integral Equations 4, 30-41 2016

  • 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

  • On Numerical Treatments to Solve a Volterra–Hammerstein Integral Equation
    SA Raad
    BJMCS 14 (6), 1-15 2016

  • On a Discussion of Fredholm – Urysohn integral equation with singular kernel in time
    MMEKSA Raad
    Universal Journal of Integral Equations 3, 51-60 2015

  • Nonlocal solution of mixed integral equation with singular kernel
    MA Abdou, SA Raad, W Wahied
    Global Journal of Science Frontier Research 15, 56-67 2015

  • 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

  • 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

  • Fundamental contact problem and singular mixed integral equation
    MA Abdou, S Raad, S Al-Hazmi
    Life Sci. J. 8, 323-329 2014

  • 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

  • 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

  • Fredholm–Volterra integral equations with logarithmic kernel
    M Abdou, S Raad
    J. Appl. Math. Comput 176, 215-224 2006

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
    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
    Citations: 13

  • New numerical approach for the nonlinear quadratic integral equations
    MA Abdou, SA Raad
    Journal of Computational and Theoretical Nanoscience 13 (10), 6435-6439 2016
    Citations: 6

  • Toeplitz matrix and Nystrm method for solving linear fractional integro-differential equation
    S Raad, K Alqurashi
    European Journal of Pure and Applied Mathematics 15 (2), 796-809 2022
    Citations: 4

  • Nonlocal solution of mixed integral equation with singular kernel
    MA Abdou, SA Raad, W Wahied
    Global Journal of Science Frontier Research 15, 56-67 2015
    Citations: 4

  • Nystrm 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
    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
    Citations: 3

  • Fredholm–Volterra integral equations with logarithmic kernel
    M Abdou, S Raad
    J. Appl. Math. Comput 176, 215-224 2006
    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
    Citations: 2

  • A New Numerical Treatment for the Nonlinear Quadratic Integral Equation in Two-Dimensions
    SA Raad
    Universal Journal of Integral Equations 4, 30-41 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
    Citations: 2

  • On Numerical Treatments to Solve a Volterra–Hammerstein Integral Equation
    SA Raad
    BJMCS 14 (6), 1-15 2016
    Citations: 2

  • 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
    Citations: 2