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ijs-3854
Variational Approximate Solutions of Fractional Delay Differential Equations with Integral Transform
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     The idea of the paper is to consolidate Mahgoub transform and variational iteration method (MTVIM) to solve fractional delay differential equations (FDDEs). The fractional derivative was in Caputo sense. The convergences of approximate solutions to exact solution were quick. The MTVIM is characterized by ease of application in various problems and is capable of simplifying the size of computational operations.  Several non-linear (FDDEs) were analytically solved as illustrative examples and the results were compared numerically. The results for accentuating the efficiency, performance, and activity of suggested method were shown by comparisons with Adomian Decomposition Method (ADM), Laplace Adomian Decomposition Method (LADM), Modified Adomian Decomposition Method (MADM) and Homotopy Analysis Method (HAM).

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Publication Date
Sun Apr 30 2023
Journal Name
Iraqi Journal Of Science
Numerical and Analytical Solutions of Space-Time Fractional Partial Differential Equations by Using a New Double Integral Transform Method
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  This work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.

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Publication Date
Sat Oct 01 2022
Journal Name
Journal Of Computational Science
Novel approximate solution for fractional differential equations by the optimal variational iteration method
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Publication Date
Sat Oct 01 2022
Journal Name
Journal Of Computational Science
Novel approximate solution for fractional differential equations by the optimal variational iteration method
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Publication Date
Wed May 17 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Extend Differential Transform Methods for Solving Differential Equations with Multiple Delay
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In this paper, we present an approximate analytical and numerical solutions for the differential equations with multiple delay using the extend differential transform method (DTM). This method is used to solve many linear and non linear problems.

 

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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
Sun Oct 22 2023
Journal Name
Iraqi Journal Of Science
Variational Iteration Method for Solving Multi-Fractional Integro Differential Equations
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In this paper, we present an approximate method for solving integro-differential equations of multi-fractional order by using the variational iteration method.
First, we derive the variational iteration formula related to the considered problem, then prove its convergence to the exact solution. Also we give some illustrative examples of linear and nonlinear equations.

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Publication Date
Wed Jul 17 2019
Journal Name
Iraqi Journal Of Science
An Approximation Technique for Fractional Order Delay Differential Equations
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In this research article, an Iterative Decomposition Method is applied to approximate linear and non-linear fractional delay differential equation. The method was used to express the solution of a Fractional delay differential equation in the form of a convergent series of infinite terms which can be effortlessly computable.
The method requires neither discretization nor linearization. Solutions obtained for some test problems using the proposed method were compared with those obtained from some methods and the exact solutions. The outcomes showed the proposed approach is more efficient and correct.

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Publication Date
Sun Aug 13 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Numerical Solutions of Fractional Integral and Fractional Integrodifferential Equations
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 In this paper, we introduce and discuss an algorithm for the numerical solution of some kinds of fractional integral and fractional integrodifferential equations. The algorithm for the numerical solution of these equations is based on iterative approach. The stability and convergence of the fractional order numerical method are described. Finally, some numerical examples are provided to show that the numerical method for solving the fractional integral and fractional integrodifferential equations is an effective solution method.

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Publication Date
Sat May 08 2021
Journal Name
Iraqi Journal Of Science
The Numerical Solutions of Nonlinear Time-Fractional Differential Equations by LMADM
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This paper presents a numerical scheme for solving nonlinear time-fractional differential equations in the sense of Caputo. This method relies on the Laplace transform together with the modified Adomian method (LMADM), compared with the Laplace transform combined with the standard Adomian Method (LADM). Furthermore, for the comparison purpose, we applied LMADM and LADM for solving nonlinear time-fractional differential equations to identify the differences and similarities. Finally, we provided two examples regarding the nonlinear time-fractional differential equations, which showed that the convergence of the current scheme results in high accuracy and small frequency to solve this type of equations.

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Publication Date
Thu May 30 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Analytical approximate solutions of random integro differential equations with laplace decomposition method
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An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

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