Solution for generalized fuzzy fractional Kortewege-de Varies equation using a robust fuzzy double parametric approach

Verma, Lalchand; Meher, Ramakanta; Avazzadeh, Z.; Nikan, O.

doi:10.1016/j.joes.2022.04.026

Cited by 17 publications

(10 citation statements)

References 32 publications

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“…where f 0 (η) is chosen to satisfy boundary conditions (6). Substituting (10) and ( 11) in (5) gives Subject to conditions, we obtain…”

Section: Spectral Adomian Decomposition Methods (Sadm)mentioning

confidence: 99%

“…Some of these methods are facing a limitation in their accuracy, efciency, and stability. To remove these limitations, several researchers used many perturbation or nonperturbation methods such as the Lyapunov artifcial small parameter method [1], homotopy perturbation method [2,3], homotopy analysis method [4], numerical methods of diferent type fuzzy equations [5][6][7][8][9], Volterra-Fredholm integral equations [10,11], fractional diferential equations (12) and (13), and Adomian decomposition method [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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The Spectral Adomian Decomposition Method for the Solution of MHD Jeffery–Hamel Problem

Khidir

2023

Mathematical Problems in Engineering

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In this study, the effects of magnetic field on the Jeffery–Hamel problem is studied using a powerful numerical method called the spectral Adomian decomposition method (SADM). The traditional Navier–Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. Comparisons with the numerical solutions are made to demonstrate the validity and high accuracy of the present approach. The velocity profile of the inner part of the divergent channel is studied for various values of magnetic field parameter and angle of channel. It was found that an increase in the magnetic field parameter leads to increase in the velocity profile. The results indicated that this technique is more efficient and converges faster than the standard Adomian decomposition method.

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“…where f 0 (η) is chosen to satisfy boundary conditions (6). Substituting (10) and ( 11) in (5) gives Subject to conditions, we obtain…”

Section: Spectral Adomian Decomposition Methods (Sadm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Spectral Adomian Decomposition Method for the Solution of MHD Jeffery–Hamel Problem

Khidir

2023

Mathematical Problems in Engineering

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“…Now by applying the Generalized transform in Caputo sense [48] in equation (3.30), we get Upon simplifying the equation (3.32), we get…”

Section: Fuzzy Computation In Caputo Sensementioning

confidence: 99%

Numerical approach on time-fractional Sawada-Kotera equation based on fuzzy extension of generalized dual parametric homotopy algorithm

Al-Saedi,

Verma,

Meher

et al. 2024

Phys. Scr.

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‎This paper considers a fuzzy nonlinear fifth-order time-fractional Sawada-Kotera equation with a singular kernel and a non-singular Mittag-Leffler kernel‎. ‎The proposed fractional differential equation is discussed with the Caputo and ABC fractional derivative under strongly generalized results and with fuzzy modelling‎. ‎A novel double parametric approach‎, ‎i.e.‎, ‎q-homotopy analysis generalized transform method (q-HAGTM)‎, ‎is considered to find the solution of the proposed model with Caputo and ABC fractional derivatives‎. ‎The problem's uniqueness and convergence analysis are investigated using Banach's fixed point theorem‎. ‎Finally‎, ‎the numerical results have been validated by comparing them with the available results in Caputo and ABC sense under strongly generalized derivatives in the crisp case‎.

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“…A fuzzy set in ,is a function ,where is the set of real numbers and a set of order pairs.It can be written as mathematically 44 as where C is the membership value.…”

Section: Preliminariesmentioning

confidence: 99%

Effect of heat transfer on hybrid nanofluid flow in converging/diverging channel using fuzzy volume fraction

Verma

Meher

Hammouch

et al. 2022

Sci Rep

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This work explores the magneto-hydrodynamics (MHD) Jeffery–Hamel nanofluid flow between two rigid non-parallel plane walls with heat transfer by employing hybrid nanoparticles, especially Cu and Cu-Al$$_{2}$$ 2 O$$_{3}$$ 3 . Here the MHD nanofluid flow problem is extended with fuzzy volume fraction and heat transfer with diverse nanoparticles to cover the influence of thermal profiles with hybrid nanoparticles on the fuzzy velocity profiles. The nanoparticle volume fraction is described with a triangular fuzzy number ranging from 0 to $$5\%$$ 5 % . A novel double parametric form-based homotopy analysis approach is considered to study the fuzzy velocity and temperature profiles with hybrid nanoparticles in both convergent and divergent channel positions. Finally, the efficiency of the proposed method has been demonstrated by comparing it with the available results in a crisp environment for validation.

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Solution for generalized fuzzy fractional Kortewege-de Varies equation using a robust fuzzy double parametric approach

Cited by 17 publications

References 32 publications

The Spectral Adomian Decomposition Method for the Solution of MHD Jeffery–Hamel Problem

The Spectral Adomian Decomposition Method for the Solution of MHD Jeffery–Hamel Problem

Numerical approach on time-fractional Sawada-Kotera equation based on fuzzy extension of generalized dual parametric homotopy algorithm

Effect of heat transfer on hybrid nanofluid flow in converging/diverging channel using fuzzy volume fraction

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