Osama H. Mohammed

Al-Nahrain University/ College of Science · Department of Mathematics and Computer Applications

This work focuses on providing an efficient well known method which is so called Adomain decom�position method for solving non-linear delay fuzzy fractional variable-order partial differential equations. The fractional order derivative will be in the Caputo sense. According to this method, the solution can be simply com�puted as a components of a c...

In this study, the Perturbation Iteration transform method, namely PITM, is in short presented and implemented for solving a class of fractional integro-differential equations. The fractional derivative will be in the Atangana– Baleanu Caputo fractional derivative sense (ABC). The (PITM) is consists of merging Laplace transform method and the pertu...

This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to...

In this paper, we introduce an approximate method for solving fractional order delay variational problems using fractional Euler polynomials operational matrices. For this purpose, the operational matrices of fractional integrals and derivatives are designed for Euler polynomials. Furthermore, the delay term in the considered functional is also dec...

In this article, we present an effective approach for solving nonlinear fractional order integro-differential equations. The fractional order derivative will be in the Caputo sense. For this, we propose an approach combined the least squares method together with the Laplace transform and the shifted Legendre polynomials. Using the proposed approach...

In this paper, a developed technique of homotopy analysis method (HAM) is presented to solve nonlinear system of fractional order Volterra integro-differential equations. The fractional derivative is described in the Caputo form. The main thing we have done in this paper is that we have simplified the process of evaluating the fractional order inte...

In this paper, Chebyshev operational matrices collocation technique is proposed for solution of variable order derivative within the fractional time-delay diffusion equation. The beginning of this approach is based on the construction of the solution using the shifted Chebyshev polynomials with unknown coefficients. After that, we performed the New...

The homotopy perturbation method is extend to derive the approximate solution of the variable order fractional partial differential equations with time delay. The variable order fractional derivative is taken in the Caputo sense. An approximation formula of the Caputo derivative of fractional variable order is presented in terms of standard (intege...

This article adopts a novel technique to numerical solution for fractional time-delay diffusion equation with variable-order derivative (VFDDEs). As a matter of fact, the variable-order fractional derivative (VFD) that has been used is in the Caputo sense. The first step of this technique is constructive on the construction of the solution using th...

This article adopts a novel technique to numerical solution for fractional time-delay diffusion equation with variable-order derivative (VFDDEs). As a matter of fact, the variable-order fractional derivative (VFD) that has been used is in the Caputo sense. The first step of this technique is constructive on the construction of the solution using th...

In this paper, we will use an artificial neural network (ANN) to solve the variable order fractional integro-differential algebraic equations (VFIDAEs), which is a three-layer feed-forward neural architecture that is formed and trained using a backpropagation unsupervised learning algorithm based on the gradient descent rule for minimizing the erro...

In this paper, we introduce two reliable efficient approximate methods for solving a class of fractional Lane–Emden equations with conformable fractional derivative (CL-M) which are the so-called conformable Homotopy–Adomian decomposition method (CH-A) and conformable residual power series method (CRP). Furthermore, the proposed methods express the...

In this article, an efficient reliable method, which is the residual power series method (RPSM), is used in order to investigate the approximate solutions of conformable time fractional nonlinear evolution equations with conformable derivatives under initial conditions. In particular, two types of equations are considered, which are time coupled di...

In this article, we offer an easy and active computational technique for finding the solution of the fractional order Sturm-Liouville problems (FOSLPs) with variable coefficients using operational matrices of (BPs). The fractional order derivatives (FODs) are characterized in the Caputo sense. The proposed technique transform the fractional order d...

In this paper, we considered nonlinear systems of fractional order differential equations. They have been solved by a computational methods which are so-called Laplace Adomian decomposition method (LADM) and modified Laplace decomposition method (MLDM). The fractional derivatives are described in the Caputo sense. The (LADM) and the (MLDM) are a co...

In this paper, a simple algorithm is applied to the systems of linear integro-differential equations of fractional order, the fractional derivative is described in the Caputo sense. The applied algorithm consists of a single series in which the unknown constants are determined by the simple means described in the manuscript. Some illustrative examp...

In this article the numerical solution of thin plates problem is introduced by using the differential quadrature method together with Chebyshev Gauss Lobatto sampling points for modeling the vibration of a square thin plate. The explicit formula of the weighting coefficients for approximation of derivatives is utilized with the aid of the G-spline...

In this article, a Legendre wavelet-Chebyshev wavelet spectral collocation method is proposed for solving fractional order space-time Burger's equation with the Legendre wavelet and Chebyshev wavelet operational matrices of fractional derivatives. The fractional derivative is described in the Caputo sense. The proposed method is based on Legendre w...

In this article, a Legendre wavelet- Chebyshev wavelet spectral collocation method is proposed for solving fractional order space-time Burger's equation with the Legendre wavelet and Chebyshev wavelet operational matrices of fractional derivatives. The fractional derivative is described in the Caputo sense. The proposed method is based on Legendre...

In this paper, approximation techniques based on the shifted Jacobi together with spectral tau technique are presented to solve a class of initial-boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain. The fractional derivatives are described in the Caputo sense. The technique is derived by exp...

This paper presents a numerical technique for solving a class of fractional variational problems using a direct method based on operational matrix of generalized hat basis function. The fractional derivative is defined in the Caputo sense.Minimization of such functional leads to a set of algebraic equations which are solved using an appropriate num...

In this paper, we present an approximate solution for fuzzy integro-differential equations of fractional order of the form: 0 0 x q *x 0 0 x

In this paper the numerical solution of fractional diffusion wave equation is proposed. The fractional derivative will be in the Caputo sense. The proposed method will be based on shifted Legendre collocation scheme and sinc function approximation for time and space respectively. The problem is reduced to the problem into a system of algebraic equa...

In this paper, we present a numerical method for fractional diffusion equations with variable coefficients. This method is based on Shifted Jacobi collocation scheme and Sinc functions approximation for temporal and spatial discretizations, respectively. The method consists of reducing the problem to the solution of linear algebraic equations by ex...

In this paper, a modified numerical algorithm for solving the fractional diffusion equation is proposed. Based on Tau idea where the shifted Legendre polynomials in time and the shifted Chebyshev polynomials in space are utilized respectively. The problem is reduced to the solution of a system of linear algebraic equations. From the computational p...

In this paper, approximation techniques based on the shifted Jacobi together with spectral tau technique are presented to solve a class of initial-boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain. The fractional derivatives are described in the Caputo sense. The technique is derived by exp...

In this paper, fuzzy multi-objective optimization problems with constraints are presented. The weighting method is considered to formulate the fuzzy multi-objective optimization problem as a fuzzy single-objective function and then Iskandars' approach is used to transform the fuzzy single-objective linear programming problem into an equivalent cris...

In this paper, Bernstein piecewise polynomial is used to approximate the solution of the fractional integro-differential equations, in which the fractional derivative is described in the (Caputo) sense. Examples are considered to verify the effectiveness of the proposed derivation, and the approximate solutions guarantee the desired accuracy.

In this paper we present an approximate analytical solution for fuzzy fractional initial value problems (FFIVP's) of the form: y (q) (x) f(x, y(x)), p 1 < q p, p y (j) (a) ja y , j 0, 1, …, p 1 where the fuzzyness appeared in the initial conditions, to be fuzzy numbers, using the differential transform method. The solution of our model equations ar...