On solution of fuzzy Volterra integro-differential equations

Ullah, Zia; Ahmad, Shabir; Ullah, Aman; Akgül, Ali

doi:10.1080/25765299.2021.1970874

Cited by 5 publications

(2 citation statements)

References 36 publications

(45 reference statements)

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“…Abdul Majid et al (2) solved the fuzzy Volterra-integro differential equations using the general linear method. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Savla,

Sharmila

2024

IJST

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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

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Section: Introductionmentioning

confidence: 99%

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

Savla,

Sharmila

2024

IJST

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“…An engineer can foresee possible form changes of the plate in vibrations based on the equations mentioned earlier in simulation findings. Numerous engineering problems fall into this category by nature, and engineers should address them using numerical approaches; see for more details [20,21].…”

Section: Introductionmentioning

confidence: 99%

Analytical Fuzzy Analysis of a Fractional-Order Newell-Whitehead-Segel Model with Mittag-Leffler Kernel

Alkhezi

Shah

Ntwiga

2022

Journal of Function Spaces

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In this paper, the method for evaluating an analytical solution of fuzzy Newell-Whitehead-Segel equation with certain affecting terms of force has been given. The notions of an Atangana-Baleanu-Caputo derivative in the vague or uncertainty form are used to reach this type of result for the solution as mentioned earlier. The fuzzy Laplace transformation is implemented at the first attempt to achieve the series form result. Secondly, the iterative method is applied to investigate the suggested solution by inverse Laplace transform. Some new solutions on the Laplace transform of an arbitrary derivative under uncertainty are presented. The solution has been provided in terms of infinite series for the research, which reduces the problem to a few equations. The required results are then calculated in a series solution form that quickly leads to the analytical answer. The solution is divided into two sections, or fuzzy branches, the lower and upper branches. We proved certain test problems to demonstrate the effectiveness of the recommended approach.

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A Quantitative Approach to $$n{\text {th}}$$-Order Nonlinear Fuzzy Integro-Differential Equation

Haq

Ullah

Ahmad

et al. 2022

Int. J. Appl. Comput. Math

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On solution of fuzzy Volterra integro-differential equations

Cited by 5 publications

References 36 publications

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

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

Analytical Fuzzy Analysis of a Fractional-Order Newell-Whitehead-Segel Model with Mittag-Leffler Kernel

A Quantitative Approach to $$n{\text {th}}$$-Order Nonlinear Fuzzy Integro-Differential Equation

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