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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
Thu Dec 02 2021
Journal Name
Iraqi Journal Of Science
Approximate Solution for advection dispersion equation of time Fractional order by using the Chebyshev wavelets-Galerkin Method
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The aim of this paper is adopted to give an approximate solution for advection dispersion equation of time fractional order derivative by using the Chebyshev wavelets-Galerkin Method . The Chebyshev wavelet and Galerkin method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are described based on the Caputo sense. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Study of Telegraph Equation via He-Fractional Laplace Homotopy Perturbation Technique
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A new technique to study the telegraph equation, mostly familiar as damped wave equation is introduced in this study. This phenomenon is mostly rising in electromagnetic influences and production of electric signals.  The proposed technique called as He-Fractional Laplace technique with help of Homotopy perturbation is utilized to found the exact and nearly approximated results of differential model and numerical example of telegraph equation or damped wave equation in this article. The most unique term of this technique is that, there is no worry to find the next iteration by integration in recurrence relation. As fractional Laplace integral transformation has some limitations in non-linear terms, to get the result of nonlinear term in

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Publication Date
Fri Mar 01 2024
Journal Name
Baghdad Science Journal
Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operator
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The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of

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Publication Date
Thu Apr 26 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation
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In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

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Publication Date
Fri Jan 01 2016
Journal Name
Applied And Computational Mathematics
Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets
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Publication Date
Tue May 01 2018
Journal Name
Journal Of Physics: Conference Series
The Approximate Solution of Fractional Damped Burger’s Equation and its Statistical Properties
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Publication Date
Thu Jul 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Analytical Solutions to Investigate Fractional Newell-Whitehead Nonlinear Equation Using Sumudu Transform Decomposition Method
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Some nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems

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Publication Date
Tue Mar 30 2021
Journal Name
Baghdad Science Journal
Solvability of Some Types for Multi-fractional Integro-Partial Differential Equation
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In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions. 

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Publication Date
Tue Jun 20 2023
Journal Name
Baghdad Science Journal
Numerical Solutions for the Nonlinear PDEs of Fractional Order by Using a New Double Integral Transform with Variational Iteration Method
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This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

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Publication Date
Mon May 15 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Finite Difference Method for Two-Dimensional Fractional Partial Differential Equation with parameter
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 In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional partial differential equation with parameter. The algorithm for the numerical solution of this equation is based on implicit and an explicit difference method. Finally, numerical example is provided to illustrate that the numerical method for solving this equation is an effective solution method.

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