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The Numerical Approximation of the Bioheat Equation of Space-Fractional Type Using Shifted Fractional Legendre Polynomials
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The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

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Publication Date
Tue Mar 30 2021
Journal Name
Iraqi Journal Of Science
Wang-Ball Polynomials for the Numerical Solution of Singular Ordinary Differential Equations
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This paper presents a new numerical method for the solution of ordinary differential equations (ODE). The linear second-order equations considered herein are solved using operational matrices of Wang-Ball Polynomials. By the improvement of the operational matrix, the singularity of the ODE is removed, hence ensuring that a solution is obtained. In order to show the employability of the method, several problems were considered. The results indicate that the method is suitable to obtain accurate solutions.

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Publication Date
Wed Jan 22 2020
Journal Name
Iraqi Journal Of Laser
Stress Urinary Incontinence Treatment Using Vaginal Fractional CO2 Laser (10600nm)
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Stress urinary incontinence (SUI) is involuntary urine leakage during activities that increase abdominal pressure such as coughing, sneezing and lifting of heavy weights. This is a very common disorder among women with history of multiple vaginal deliveries with an obstructed labor. SUI is considered one of the most distressing problems, especially for younger women, with severe quality of life implications, it caused by the loss of urethral support, usually as a consequence of the supporting structural muscles in the pelvis.

Objective: To prove and demonstrate the effect of a fractional CO2 micro-ablative laser (10600nm) in intra vaginal therapy for treating SUI and achieve a clinical improvement of t

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Publication Date
Sun Dec 07 2014
Journal Name
Baghdad Science Journal
Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations
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In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

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Publication Date
Wed Nov 30 2022
Journal Name
Iraqi Journal Of Science
Pointwise Estimates for Finding the Error of Best Approximation by Spline, Positive Algebraic Polynomials and Copositive
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     The first step in this research is to find some of the necessary estimations in approximation by using certain algebraic polynomials, as well as we use certain specific points in approximation. There are many estimations that help to find the best approximation using algebraic polynomials and geometric polynomials. Throughout this research, we deal with some of these estimations to estimate the best approximation error using algebraic polynomials where the basic estimations in approximation are discussed and proven using algebraic polynomials that are discussed and proven using algebraic polynomials that are specified by the following points and  if   as well as if   .

  For the second step of the work, the estimatio

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Publication Date
Wed Jan 01 2020
Journal Name
Periodicals Of Engineering And Natural Sciences
Fractional Brownian motion inference of multivariate stochastic differential equations
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Recently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical development of financial mechanism across time. Multivariate wiener process represents the stochastic term in a system of stochastic differential equations (SDE). The standard wiener process follows a Markov chain, and hence it is a martingale (kind of Markov chain), which is a good integrator. Though, the fractional Wiener process does not follow a Markov chain, hence it is not a good integrator. This problem will produce an Arbitrage (non-equilibrium in the market) in the predicted series. It is undesired property that leads to erroneous conc

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Publication Date
Sun Dec 30 2007
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Prediction of Fractional Hold-Up in RDC Column Using Artificial Neural Network
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In the literature, several correlations have been proposed for hold-up prediction in rotating disk contactor. However,
these correlations fail to predict hold-up over wide range of conditions. Based on a databank of around 611
measurements collected from the open literature, a correlation for hold up was derived using Artificial Neiral Network
(ANN) modeling. The dispersed phase hold up was found to be a function of six parameters: N, vc , vd , Dr , c d m / m ,
s . Statistical analysis showed that the proposed correlation has an Average Absolute Relative Error (AARE) of 6.52%
and Standard Deviation (SD) 9.21%. A comparison with selected correlations in the literature showed that the
developed ANN correlation noticeably

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Publication Date
Fri Jan 26 2024
Journal Name
Iraqi Journal Of Science
Effect of Mhd on Accelerated Flows of A Viscoelastic Fluid with The Fractional Burgers’ Model
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In this paper, we studied the effect of magnetic hydrodynamic (MHD) on accelerated flows of a viscoelastic fluid with the fractional Burgers’ model. The velocity field of the flow is described by a fractional partial differential equation of fractional order by using Fourier sine transform and Laplace transform, an exact solutions for the velocity distribution are obtained for the following two problems: flow induced by constantly accelerating plate, and flow induced by variable accelerated plate. These solutions, presented under integral and series forms in terms of the generalized Mittag-Leffler function, are presented as the sum of two terms. The first term, represent the velocity field corresponding to a Newtonian fluid, and the se

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Publication Date
Tue Feb 01 2022
Journal Name
Baghdad Science Journal
Numerical Solution for Linear State Space Systems using Haar Wavelets Method
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In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

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Publication Date
Wed Mar 18 2020
Journal Name
Baghdad Science Journal
Solving Linear Volterra – Fredholm Integral Equation of the Second Type Using Linear Programming Method
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In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

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Publication Date
Mon Jan 01 2024
Journal Name
2nd International Conference For Engineering Sciences And Information Technology (esit 2022): Esit2022 Conference Proceedings
Numerical solution to inverse coefficient problem for hyperbolic equation under overspecified condition of general integral type
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