Solution of one-dimensional fractional order partial integro-differential equations using variational iteration method

Hussain, Amina Kassim; Rusli, Noradila; Fadhel, Fadhel Subhi; Yahya, Zainor Ridzuan

doi:10.1063/1.4965216

Cited by 5 publications

(2 citation statements)

References 22 publications

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“…Several authors have previously stated such equations and studied their theoretical or numerical solutions. The He's approximation methods, which include the Homotopy Analysis Method (HAM), [1,3,8,13], Homotopy Perturbation Method (HPM), [9], Variational Iteration Method (VIM), [6,10], are among the approximate analytical methods used for solving differential equations in operator form with fractional derivatives or integrals.…”

Section: Introductionmentioning

confidence: 99%

Homotopy Analysis Method for Solving Multi-Fractional Order Random Ordinary Differential Equations

Mohammed,

Fadhel,

Hussain

2023

JUAPS

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The main objective of this paper is to present random ordinary differential equations with multi fractional derivatives and to use the homotopy analysis method to approximate the solution of such equations with different generations of the Weiner process or Brawnian motion. One of the most important and efficient methods for solving various mathematical problems with different operators, linear and nonlinear, ordinary or partial differential equations, integral equations, and so on, is the homotopy analysis method.

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Section: Introductionmentioning

confidence: 99%

Homotopy Analysis Method for Solving Multi-Fractional Order Random Ordinary Differential Equations

Mohammed,

Fadhel,

Hussain

2023

JUAPS

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“…Awawdeh et al [21] utilized the homotopy analysis approximation to solve the linear FPIDE analytically. Hussain et al [22] solved the FPIDE analytically by the variation iteration method. Mittal and Nigam [23] implemented the Adomian decomposition method to handle the FPIDE.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

2021

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Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.

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New method for solving fractional partial integro-differential equations by combination of Laplace transform and resolvent kernel method

Loh

Phang

Tay

2020

Chinese Journal of Physics

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Solution of one-dimensional fractional order partial integro-differential equations using variational iteration method

Cited by 5 publications

References 22 publications

Homotopy Analysis Method for Solving Multi-Fractional Order Random Ordinary Differential Equations

Homotopy Analysis Method for Solving Multi-Fractional Order Random Ordinary Differential Equations

A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

New method for solving fractional partial integro-differential equations by combination of Laplace transform and resolvent kernel method

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