Variational Iteration Method and Adomian Decomposition Method for Fourth-Order Fractional Integro-Differential Equations

Amer, S. M.; Saleh, M. H.; Mohamed, Maizan; Abdelrhman, N. S.

doi:10.5120/13863-1718

Cited by 5 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to the difficulty and impossibility in obtaining precise solutions for a lot of FDEs and FIDEs, some researchers and scholars use numerical or approximate solution approaches to get the solution to these problems. Among the approximate approaches used by some researchers for FDEs and FIDEs are homotopic analysis (HAM) and optimum q-homotopic analysis method (Oq-HAM) [11,12], optimal homotopic perturbation (OHPM) and homotopic perturbation method (HPM) [13,14], Adomian's decomposition method (ADM) [15], variational iteration method (VIM) [13,15] and collocation approach [16,17], etc. [18,19].…”

Section: • Controlmentioning

confidence: 99%

Approximate solution for high-order fractional integro-differential equations via trigonometric basic functions

Agheli

Firozja

2019

Sādhanā

View full text Add to dashboard Cite

An approach for searching an approximate solution of high-order integro-differential equations featuring fractional derivatives has been proposed in this paper. Initially, using trigonometric basic functions (TBFs), we determine the transformation functions in association to TBFs. Next, the approximate function is presented as a combination of TBFs and transform functions. The convergence of this approach is also presented. Using discrete derivatives of the solution to gain an approximate solution, we find the approximate solution, which satisfies the high-order integro-differential equations featuring fractional derivatives. An algorithm of this approach is applied for various examples, and one example is illustrated in detail.

show abstract

Section: • Controlmentioning

confidence: 99%

Approximate solution for high-order fractional integro-differential equations via trigonometric basic functions

Agheli

Firozja

2019

Sādhanā

View full text Add to dashboard Cite

show abstract

“…Numerical and analytical methods have been used to solve this type of equation such as homotopy perturbation method [7], variational iteration method [7,8], homotopy analysis method [9], and Adomian decomposition method [8].…”

Section: Introductionmentioning

confidence: 99%

New Approach of Modifying Laplace Transform Variational Iteration Method to solve Fourth-Order Fractional Integro-Differential Equations

Hailat,

Zainuddin,

Azmi

2024

Preprint

View full text Add to dashboard Cite

In this paper, nonlinear boundary value problems for fourth-order fractional integro-differential equations are solved by modified Laplace transform variational iteration method (MLT-VIM). This modification is designed to improve the accuracy of the approximate solutions obtained by LT-VIM. The suitable initial approximation will be selected based on a rule or standard to adjust the determination of the initial guess that satisfies the boundary conditions. Furthermore, the residual error will be cancelled at several points of the appropriate interval. The convergence conditions of the proposed method are investigated. Some illustrative examples of nonlinear boundary value problems for fourth-order fractional integro-differential equations are presented in order to demonstrate the effectiveness of the proposed method. Comparisons are made between the results obtained by MLT-VIM and LT-VIM depending on the exact solutions, revealing that the MLT-HPM contributes to reduce the amount of computational work to obtain the first-order approximate solution which greatly accelerates the convergence of the solution. Whereas LT-HPM needs more iterations to obtain a suitable approximate solution, which results in an increase in the computational workload.

show abstract

“…Also, based on the Haar wavelet collocation method, Marasi and Derakhshan in [20] focused on finding a numerical method for solving the variableorder Caputo-Prabhakar FracIDEs. Higher order FracIDEs, such as the fourth-order FracIDEs, were solved by Amer et al [5] using the Adomian decomposition method (ADM) and variational iteration method (VIM), where the solution was given by an infinite convergent series. Also, quite a few approximated techniques described in [9,24] have been discussed in the past to solve the linear and nonlinear FracIDEs.…”

Section: Introductionmentioning

confidence: 99%

Numerical Treatment of Volterra-Fredholm Integro- Differential Equations of Fractional Order and its Convergence Analysis

PANDA,

MOHAPATRA

2024

KgJMat

View full text Add to dashboard Cite

This work deals with semi-analytical and numerical methods to solve a class of fractional order Volterra-Fredholm integro-diﬀerential equations. First, a semi-analytical method is proposed using the Chebyshev and Bernstein polynomials in the Adomian decomposition method. The uniqueness of the solution and convergence of the method are proved. Further, we solve the model using a numerical scheme comparing the L1 scheme for the fractional order derivative in combination with appropriate quadrature rules for the integral parts. Numerical experiments are done by the proposed methods to show their eﬃciency through a few tabular data and plots. Some comparisons with the existing results show that the proposed methods are highly productive and reliable.

show abstract

Variational Iteration Method and Adomian Decomposition Method for Fourth-Order Fractional Integro-Differential Equations

Cited by 5 publications

References 12 publications

Approximate solution for high-order fractional integro-differential equations via trigonometric basic functions

Approximate solution for high-order fractional integro-differential equations via trigonometric basic functions

New Approach of Modifying Laplace Transform Variational Iteration Method to solve Fourth-Order Fractional Integro-Differential Equations

Numerical Treatment of Volterra-Fredholm Integro- Differential Equations of Fractional Order and its Convergence Analysis

Contact Info

Product

Resources

About