Study of Nonlinear Fuzzy Integro-differential Equations Using Mathematical Methods and Applications

Ahmad, Jamshad; Iqbal, Angbeen; Hassan, Qazi Mahmood Ul

doi:10.5391/ijfis.2021.21.1.76

Cited by 10 publications

(3 citation statements)

References 16 publications

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“…Devi and Ganesan used fuzzy differential equations in modelling electric circuit problem [9]. Ahmad et al [10] studied a mathematical method to fnd the solution of fuzzy integro-diferential equations. Sadeghi et al [11] studied the system of fuzzy diferential equation.…”

Section: Introductionmentioning

confidence: 99%

Techniques for Finding Analytical Solution of Generalized Fuzzy Differential Equations with Applications

et al. 2023

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Engineering and applied mathematics disciplines that involve differential equations include classical mechanics, thermodynamics, electrodynamics, and general relativity. Modelling a wide range of real-world situations sometimes comprises ambiguous, imprecise, or insufficient situational information, as well as multiindex, uncertainty, or restriction dynamics. As a result, intuitionistic fuzzy set models are significantly more useful and versatile in dealing with this type of data than fuzzy set models, triangular, or trapezoidal fuzzy set models. In this research, we looked at differential equations in a generalized intuitionistic fuzzy environment. We used the modified Adomian decomposition technique to solve generalized intuitionistic fuzzy initial value problems. The generalized modified Adomian decomposition technique is used to solve various higher-order generalized trapezoidal intuitionistic fuzzy initial value problems, circuit analysis problems, mass-spring systems, steam supply control sliding value problems, and some other problems in physical science. The outcomes of numerical test applications were compared to exact technique solutions, and it was shown that our generalized modified Adomian decomposition method is efficient, robotic, and reliable, as well as simple to implement.

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Section: Introductionmentioning

confidence: 99%

Techniques for Finding Analytical Solution of Generalized Fuzzy Differential Equations with Applications

et al. 2023

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“…Devi et al used fuzzy differential equations in modelling electric circuit problem [7]. Ahmad et al [8] studied a mathematical method to find the solution of fuzzy integro differential equations. Sadeghi at al [9] studied the system of fuzzy differential equation.…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Scheme for Solving Intuitionistic Fuzzy System of Differential Equations

et al. 2023

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The aim of this article is to implement the Generalized Modified Adomian Decomposition Method to compute the semi-numerical solution of the linear system of intuitionistic fuzzy initial value problems. Here, we consider the initial values as generalized trapezoidal intuitionistic fuzzy numbers. The technique is applied to brine tanks problem and coupled mass spring systems.Theoretically, different approaches to solving a system of generalized trapezoidal intuitionistic fuzzy differential equations are discussed in this study under the presumption that the coefficients of the system of the differential equations are associated to generalized trapezoidal intuitionistic fuzzy numbers. The approximate results are compared with exact solutions which shows good efficiency. The corresponding graphs at different levels of uncertainty show the example's numerical outcomes. The graphical representations further demonstrate the effectiveness and accuracy of the proposed method in comparison to existing semi-numerical methods in the literature. INDEX TERMSFuzzy set; Fuzzy number; Generalized trapezoidal intuitionistic fuzzy number; System of Fuzzy differential equation; Analytical technique; Engineering Applications.

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“…Sindu Devi and Ganesan 6 used fuzzy differential equations in modeling electric circuit problems. Ahmad et al 7 studied a mathematical method to find the solution of fuzzy integro differential equations. Sadeghi et al 8 studied the system of fuzzy differential equations.…”

Section: Introductionmentioning

confidence: 99%

Computationally semi-numerical technique for solving system of intuitionistic fuzzy differential equations with engineering applications

Shams

Kausar

Kousar

et al. 2022

Advances in Mechanical Engineering

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Some complex problems in science and engineering are modeled using fuzzy differential equations. Many fuzzy differential equations cannot be solved by using exact techniques because of the complexity of the problems mentioned. We utilize analytical techniques to solve a system of fuzzy differential equations because they are simple to use and frequently result in closed-form solutions. The Generalized Modified Adomian Decomposition Method is developed in this article to compute the analytical solution to the linear system of intuitionistic triangular fuzzy initial value problems. The starting values in this case are thought of as intuitionistic triangular fuzzy numbers. Engineering examples, such as the Brine Tanks Problem, are used to demonstrate the proposed approach and show how the series solution converges to the exact solution in closed form or in series. The corresponding graphs at different levels of uncertainty show the example’s numerical outcomes. The graphical representations further demonstrate the effectiveness and accuracy of the proposed method in comparison to Taylor’s approaches and the classical Decomposition method.

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Study of Nonlinear Fuzzy Integro-differential Equations Using Mathematical Methods and Applications

Cited by 10 publications

References 16 publications

Techniques for Finding Analytical Solution of Generalized Fuzzy Differential Equations with Applications

Techniques for Finding Analytical Solution of Generalized Fuzzy Differential Equations with Applications

Semi-Analytical Scheme for Solving Intuitionistic Fuzzy System of Differential Equations

Computationally semi-numerical technique for solving system of intuitionistic fuzzy differential equations with engineering applications

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