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Research Article Open access CC BY 4.0

The Modified Variational Iteration Method to Solve Linear Fractional Differential Equations

Nader M. Bassi, Anazeer Ismail

Journal of Advances in Mathematics and Computer Science · pp. 57–64 · Published 16 Sep 2022

10.9734/jamcs/2022/v37i830472

Abstract

In this work we conceive a method of  how the Lagrange multiplier of modified Variational Iteration Method can be defined from Laplace transform, And we use this technique to solve both differential equations and FDEs with initial value conditions,  With Illustrative examples by  applying the modified VIM to both Ordinary differential equations and fractional Differential Equations.

Variational iteration method Lagrange multiplier Laplace transform fractional differential equations Caputo derivative

References (13)

  1. 1 Variational iteration method – a kind of non-linear analytical technique: some examples [DOI]
  2. 2 Approximate analytical solution for seepage flow with fractional derivatives in porous media [DOI]
  3. 3 Variational iteration method—Some recent results and new interpretations [DOI]
  4. 4 Variational iteration method: New development and applications [DOI]
  5. 5 A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials [DOI]
  6. 6 Analytic and approximate solutions of the space- and time-fractional telegraph equations [DOI]
  7. 7 Multidimensional solutions of time-fractional diffusion-wave equations [DOI]
  8. 8 Variational iteration method for fractional calculus - a universal approach by Laplace transform [DOI]
  9. 9 Variational iteration technique for solving higher order boundary value problems [DOI]
  10. 10 Comparison between the Laplace Decomposition Method and Adomian Decomposition in Time-Space Fractional Nonlinear Fractional Differential Equations [DOI]
  11. 11 New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time-Partial Fractional Differential Equations [DOI]
  12. 12 The solution of radial diffusivity and shock wave equations by Elzaki variational iteration method [DOI]
  13. 13 The generalized (2 + 1) and (3+1)-dimensional with advanced analytical wave solutions via computational applications [DOI]

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د کسري دیفرانسیلي معادلو د حل لپاره د تغیر تکرار منونکي او آډومین تجزیوي نیمه تحليلي میتودونو پرتله

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