Faraidun k. Hamasalh | University of Sulaimani (original) (raw)

Papers by Faraidun k. Hamasalh

JOURNAL OF UNIVERSITY OF BABYLON, 2022

We propose a fractional spline method for solving fractional differential equations subject to in... more We propose a fractional spline method for solving fractional differential equations subject to initial conditions. Using the Caputo fractional integral and derivative have to construct the spline interpolation with polynomial coefficients. For the given spline function, error bounds were studied and a stability analysis was completed. The numerical explanation for the provided method was considered using three examples. The results show that the fractional spline function which interpolates data is productive and profitable in solving unique problems.

Interpolation by various types of splines is the standard procedure in many applications. In this... more Interpolation by various types of splines is the standard procedure in many applications. In this paper shall discuss the function, two and fourth derivatives of spline interpolation as an alternative to polynomial spline interpolation at the all intervals. The method is appropriate and solving of initial and boundary value problems, the results revealing that method is very effective and accurate.

In this paper, we implement new approximate techniques, the fractional lacunary interpolation by ... more In this paper, we implement new approximate techniques, the fractional lacunary interpolation by spline function for s lving differential equations of fractional order. Convergence a nalysis, existence and uniqueness are shown by several theo rems in the classes of C3 andC4 depend on the degree of spline polynomials. The numerical re sults demonstrates the errors bounds is quite validity and applicability of this method.

Annals of Translational Medicine, 2020

Background: To study the effectiveness and safety of atrial fibrillation (AF) catheter ablation a... more Background: To study the effectiveness and safety of atrial fibrillation (AF) catheter ablation after pericardiectomy. Methods: Data of 24 consecutive AF patients after pericardiectomy underwent catheter ablation from five centers were collected and analyzed retrospectively. All patients were followed up at 1, 3, and 12 months after catheter ablation. Results of a repeated blood test, electrocardiogram, and echocardiography during followup were also collected. Adverse events such as recurrence of AF, heart failure, stroke/transient ischemic attack (TIA) and minor, and major bleeding were recorded. All patients underwent brain magnetic resonance imaging (MRI) at the end of 12 months follow-up. Results: Patients were young (20-73 years old, 48.1±11.0). Fifteen (62.5%) patients were male. CHA2DS2-VASc score (0-3, 0.21±0.41) was low in these 24 patients. Among these patients, 11 (45.8%) were paroxysmal AF, 8 (33.3%) were persistent AF, and 5 (20.8%) were long-lasting persistent AF. Left atrium diameter over 45 mm was detected in 17 (70.8%) patients. All patients underwent catheter ablation successfully. No periablation procedure-related complication happened. Oral anticoagulant therapy was stopped 3 months after the final ablation. Anti-arrhythmia drugs were continued for all patients after ablation. For 12 months follow-up, AF recurred in 10 (41.7%) patients 3-7 months after the first ablation. MRI detected silent cerebral infarction (SCI) in 2 (8.3%) patients. No other adverse events occurred during follow-up. Conclusions: It is safe for AF patients to undergo catheter ablation after pericardiectomy, but the rate of recurrence of AF is high.

The aim of this paper is to investigate the performance of the ninth degree spline method for sol... more The aim of this paper is to investigate the performance of the ninth degree spline method for solving the system of ordinary differential equations and to estimate the numerical solution in the whole interval. By considering the maximum absolute errors in the solution at grid points for different choices of step size, we conclude that ninth spline produces the accurate results in comparison with other methods. AMS Subject Classification Code: 41A25, 65H10, 47E05.

Mathematical Sciences Letters, 2017

In this paper, the Bagley-Torvik equation is constructed. A model approach based on non-polynomia... more In this paper, the Bagley-Torvik equation is constructed. A model approach based on non-polynomial numerical methods spline interpolation is developed to solve some problems. W e show that the approximate solutions of such problems obtai ned by the numerical algorithm developed using non-polynomial splin e interpolation functions are better than those produced by other numerical methods. The aim of this paper is to compare the performance o f the non-polynomial spline method with polynomial spline m thod. For this purpose, the algorithm is tested on two examples to i llustrate the practical usefulness of the approach.

Mathematical Sciences Letters, 2016

In this paper, a new fractional spline method of non-polynomial form have been considered to solv... more In this paper, a new fractional spline method of non-polynomial form have been considered to solve special linear fractional boundary-value problems. Using this fractional spline function a few consistency relations are derived for computing approximations to the solution of the problem. Convergence analysis and error estimates of this methods are discussed. Numerical results are provided to demonstrate the superiority of our methods.

Abstract: Problem statement: The lacunary interpolation problem, which we had investigated in thi... more Abstract: Problem statement: The lacunary interpolation problem, which we had investigated in this study, consisted in finding the six degree spline S(x) of deficiency four, interpolating data given on the function value and third and fifth order in the interval [0,1]. Also, an extra initial condition was prescribed on the first derivative. Other purpose of this construction was to solve the second order differential equations by two examples showed that the spline function being interpolated very well. The convergence analysis and the stability of the approximation solution were investigated and compared with the exact solution to demonstrate the prescribed lacunary spline (0, 3, 5) function interpolation. Approach: An approximation solution with spline interpolation functions of degree six and deficiency four was derived for solving initial value problems, with prescribed nonlinear endpoint conditions. Under suitable assumptions, the existences; uniqueness and the error bounds of ...

The aim of this work is to construct lacunary interpolation based on quartic C 3 -spline and to a... more The aim of this work is to construct lacunary interpolation based on quartic C 3 -spline and to apply this spline function for finding approximate values of smooth function and its continuous derivatives. Upper bounds for errors and convergence analysis of the presented lacunary interpolation studied. Also, we have solved numerically two examples, to show the validity of the prescribed method by depending on the L∞-error estimation. Keywords: Lacunary interpolation model, Convergence analysis, Spline function, Quadrature, Algorithm. AMS subject classifications: 65D05, 65D07 and 65D32. Introduction In this paper, we apply quartic C 3 -spline interpolation to develop a numerical method for obtaining approximations to the value of integration, finding the error bounds and suitable assumptions with applications showed that this spline exists and is unique. The convergence analysis and the stability of the approximate solution is investigated and compared with the exact solution to illus...

Fractal and Fractional

The discrete delta Caputo-Fabrizio fractional differences and sums are proposed to distinguish th... more The discrete delta Caputo-Fabrizio fractional differences and sums are proposed to distinguish their monotonicity analysis from the sense of Riemann and Caputo operators on the time scale Z. Moreover, the action of Q− operator and discrete delta Laplace transform method are also reported. Furthermore, a relationship between the discrete delta Caputo-Fabrizio-Caputo and Caputo-Fabrizio-Riemann fractional differences is also studied in detail. To better understand the dynamic behavior of the obtained monotonicity results, the fractional difference mean value theorem is derived. The idea used in this article is readily applicable to obtain monotonicity analysis of other discrete fractional operators in discrete fractional calculus.

$Research paper thumbnail of On the generalized fractional cubic spline with application On The Generalized Fractional cubic Spline With Application$

AIP Conf. Proc. 2096, 020004-1–020004-9, 2019

Abstarct: In this paper, we introduce a generalized cubic spline method with fractional order and... more Abstarct: In this paper, we introduce a generalized cubic spline method with fractional order and study with error optimality, convergence analysis and to find out an approximate solution for fractional differential equations. This method is proposed to be applicable for α ∈ (0,1) , where a denotes the order of the fractional derivative in the Caputo sense. Error bounded of this aim is chosen and discussed, some explained example are demonstrated and also it is compared for each example that value of is changed for some values

In this paper, Fractional initial value problems y (3α) (x) = f (x, y)is solved base on the propo... more In this paper, Fractional initial value problems y (3α) (x) = f (x, y)is solved base on the proposed fractional spline interpolation for the case α, 0 < α < 1, relied on class C q −splines as a way to approximate the exact solution of such problems. In addition, this fractional spline interpolation contains β parameter, where β ∈ (0, 1] and β is taken to be equal to one to test the stability analysis of the method.

In this paper, a quintic spline interpolation algorithm presented for the solution of second orde... more In this paper, a quintic spline interpolation algorithm presented for the solution of second order initial value problems with a new class of the lacunary spline interpolation based on quintic C -splines 4 as an approximation to the exact solution of such problems. Convergence analysis of the presented spline function was discussed, stability analysis has been carried out and two examples were considered for the numerical illustration of the presented technique. The results show that the presented quintic spline function which interpolates the lacunary data was efficient and effective for solving such problems.

Problem statement: The lacunary interpolation problem, which we had investigated in this study, c... more Problem statement: The lacunary interpolation problem, which we had investigated in this study, consisted in finding the six degree spline S(x) of deficiency four, interpolating data given on the function value and third and fifth order in the interval [0,. Also, an extra initial condition was prescribed on the first derivative. Other purpose of this construction was to solve the second order differential equations by two examples showed that the spline function being interpolated very well. The convergence analysis and the stability of the approximation solution were investigated and compared with the exact solution to demonstrate the prescribed lacunary spline (0, 3, 5) function interpolation. Approach: An approximation solution with spline interpolation functions of degree six and deficiency four was derived for solving initial value problems, with prescribed nonlinear endpoint conditions. Under suitable assumptions, the existences; uniqueness and the error bounds of the spline (0, 3, 5) function had been investigated; also the upper bounds of errors were obtained. Results: Numerical examples, showed that the presented spline function proved their effectiveness in solving the second order initial value problems. Also, we noted that, the better error bounds were obtained for a small step size h. Conclusion: In this study we treated for a first time a lacunary data (0,3,5) by constructing spline function of degree six which interpolated the lacunary data (0,3,5) and the constructed spline function applied to solve the second order initial value problems.