Solving nonlinear Volterra-Fredholm fuzzy integro-differential equations by using Adomian decomposition method

Georgieva, Atanaska; Spasova, Mira

doi:10.1063/5.0041602

Cited by 1 publication

(1 citation statement)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Zia Ullah et al (3) introduced the Laplace Adomian decomposition method to find the solution of fuzzy Volterraintegro differential equations. Georgieva et al (4) used the Adomian decomposition method to solve nonlinear Volterra-Fredholm fuzzy integro-differential equations. Bargamadi et al (5) proposed the second Chebyshev wavelets method to solve the system of fractional-order Volterra-Fredholm integro differential equations with weakly singular kernels.…”

Section: Introductionmentioning

confidence: 99%

Solving Linear and Nonlinear Fuzzy Fractional Volterra-Fredholm Integro Differential Equations Using Shehu Adomian Decomposition Method

Savla,

Sharmila

2024

IJST

View full text Add to dashboard Cite

Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) and fuzzy fractional integral equations (FFIEs) are a crucial topic. The main objective of this work is to discover an analytical approximate solution for the fuzzy fractional Volterra-Fredholm integro differential equations (FFVFIDE). In the Caputo concept, fractional derivatives are regarded. Methods: The Shehu transform is challenging to exist for nonlinear problems. So, the Shehu transform is combined with the Adomian decomposition method is called the Shehu Adomian decomposition method (SHADM) and has been proposed to solve both linear and nonlinear FFVFIDEs. Findings: Both linear and nonlinear FFVIFIDEs can be solved using this technique. For nonlinear terms, Adomian polynomials have been used. The main benefit of this approach is that it converges quickly to the exact solution. Figures and numerical examples demonstrate the expertise of the suggested approach. Novelty: The comparison between the exact solution and numerical solution is shown in figures for various values of fractional order . The numerical evolution demonstrates the efficiency and reliability of the proposed SHADM. The proposed approach is rapid, exact, and simple to apply and produce excellent outcomes. Keywords: Fractional calculus, fuzzy number, Mittag Leffler function, Shehu Adomian decomposition method, fuzzy fractional Volterra-Fredholm integro differential equation

show abstract

Section: Introductionmentioning

confidence: 99%