Solution and intuitionistic fuzzy stability of 3-dimensional cubic functional equation: using two different methods

Jakhar, Jyotsana; Chugh, Renu; Jakhar, Jagjeet

doi:10.22436/jmcs.025.02.01

Cited by 5 publications

(3 citation statements)

References 21 publications

(15 reference statements)

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“…Therefore, every fixed point of the random operator (RO) F is also a random point (RP) such as the Λ-MM z : Γ → X (z(γ) = F(γ, z(γ)) for every γ ∈ Γ). Our results can extend some recent ones and improve them to obtain new results (see [12][13][14][15][16][17]).…”

Section: Preliminariessupporting

confidence: 70%

A Fuzzy Random Boundary Value Problem

Srivástava

Chaharpashlou

Saadati

et al. 2022

Axioms

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A system of generalized fuzzy random differential equations with boundary conditions is investigated, which is a fuzzy version of a system of general random differential equations. We first present random fixed point (RFP) theorems in fuzzy metric space (FM). In the sequel, we define the operators that are of integral type. Furthermore, these operators are related to a part of random differential equations (RDE). For the desired system with boundary conditions, we study the suitable integral operators associated with a large family of random differential equations. Finally, we prove the existence of a unique random solution (EURS).

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Section: Preliminariessupporting

confidence: 70%

A Fuzzy Random Boundary Value Problem

Srivástava

Chaharpashlou

Saadati

et al. 2022

Axioms

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“…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%

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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“…Fuzzy differential equations (DEs) can serve as a foundation for modeling a variety of complex systems in a fuzzy environment. [10][11][12][13][14] Zadeh 15 modified the notion of fuzzy sets to cope with data ambiguity for the first time. Later on, the fuzzy integral and differential equations, based on the idea of fuzzy sets, were developed by Zadeh to use in a variety of mathematical and computer models and to deal with uncertainty in deterministic real-world processes.…”

Section: Introductionmentioning

confidence: 99%

Solution of generalized fractional Jaulent–Miodek model with uncertain initial conditions

Sartanpara,

Meher,

Nikan

et al. 2023

AIP Advances

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This paper analyses a coupled system of generalized coupled system of fractional Jaulent–Miodek equations, including uncertain initial conditions with fuzzy extension. In this regard, an extension of the homotopy with a generalized integral algorithm is adopted for a class of time-fractional fuzzy Jaulent–Miodek models by mixing the fuzzy q-homotopy analysis algorithm with a generalized integral transform and Caputo fractional derivative. The triangular fuzzy numbers (TFNs)are expressed in double parametric form using κ-cut and r-cut and utilized to explain the uncertainties arising in the initial conditions of highly nonlinear differential equations with generalized Hukuhara differentiability (gH-differentiability). The TFNs are controlled by the κ-cut and r-cut, and the variability of uncertainty is examined using a “triangular membership function” (TMF). The results are analyzed by finding the solutions for different spatial coordinate values of time with κ-cut and r-cut for both lower and upper bounds and validated through numerical and graphical representations in crisp cases. Finally, it can be seen that the uncertain probability density function rapidly decreases at the left and right edges when the fractional order is increased, and it is observed that the obtained solutions are more accurate than the existing results through the Hermite wavelet method in the literature.

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Solution and intuitionistic fuzzy stability of 3-dimensional cubic functional equation: using two different methods

Abstract: In this article, we adopt fixed point method and direct method to find the solution and Intuitionistic fuzzy stability of 3dimensional cubic functional equation

Cited by 5 publications

References 21 publications

A Fuzzy Random Boundary Value Problem

A Fuzzy Random Boundary Value Problem

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

Solution of generalized fractional Jaulent–Miodek model with uncertain initial conditions

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