Numerical Solutions of Fuzzy Fractional Delay Differential Equations

Padmapriya, V.; Kaliyappan, M.; Manivannan, A.

doi:10.5391/ijfis.2020.20.3.247

Cited by 4 publications

(2 citation statements)

References 25 publications

(40 reference statements)

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“…The existence and uniqueness of the solution of the nonlinear FIDE and impulsive semi-linear FIDEs with nonlocal conditions and forcing the term with memory is well addressed in [12,13]. Recently, Padmapriya et al [14] investigated the numerical solutions of fuzzy fractional delay differential equations using the proposed novel technique. The HPM was first proposed by He [15,16], who also approximated the answers for several differential equations.…”

Section: Introductionmentioning

confidence: 99%

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

Ahmad¹,

Iqbal²,

Hassan³

2021

IJFIS

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In this study, the homotopy perturbation sumudu transform method (HPSTM) is employed to find the analytical fuzzy solution of nonlinear fuzzy integro-differential equations (FIDEs). The solutions of FIDEs are more generalized and have better applications. The fuzzy concept is used to overrule the uncertainty in physical models. Based on the parametric form of the fuzzy number, the nonlinear integro-differential equation (IDE) is converted into two systems of nonlinear IDEs of the second kind. Some numerical examples were solved to demonstrate the efficiency and capability of the method. Graphical representations reveal the symmetry between lower and upper cut representations of fuzzy solutions and may be helpful for a better understanding of fuzzy control models, artificial intelligence, medical science, quantum optics, measure theory, and so on.

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Section: Introductionmentioning

confidence: 99%

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

Ahmad¹,

Iqbal²,

Hassan³

2021

IJFIS

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“…Ahmad and Bibi accessed different types of fuzzy IDEs by using the approach of modified VIM [17]. Recently, Padmapriya et al investigated the numerical solutions of fuzzy fractional delay differential equations using a proposed novel technique [18].…”

Section: Introductionmentioning

confidence: 99%

Application of an Effective Method on the System of Nonlinear Fuzzy Integro-Differential Equations

2021

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In real world physical applications purpose, it is complicated to acquire an exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic and therefore creating the need for the use of reliable and efficient techniques in the solution of fuzzy differential equations. The purpose of this research paper is to utilize the reliable analytic approach of homotopy perturbation Sumudu transform method for better understanding of systems of non-linear fuzzy integro-differential equations, while using the concept of fuzzy parameter in certain dynamical problems to remove the hurdles faced in numerical approach. These mathematical models are of great interest in engineering and physics. Some numerical examples are also given to demonstrate the efficiency and superiority of the method, followed by graphical representation of the comparison of exact and approximated solution by using Maple 2017

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Artificial neural network approach for solving fuzzy fractional order initial value problems under gH‐differentiability

Ezadi

Allahviranloo

2021

Math Methods in App Sciences

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This paper aims to solve the celebrated fuzzy fractional differential equations (FFDEs) using an artificial neural network (ANN) technique. To accomplish the aforementioned aim, the error back propagation algorithm and a multilayer feed forward neural architecture are utilized using the unsupervised learning in order to minimize the error function as well as the modification of the parameters such as weights and biases. By combining the initial conditions with the ANN output provides an appropriate approximate solution of the proposed FFDE. Then, two illustrative examples are solved to confirm the applicability of the concept as well as to demonstrate both the precision and effectiveness of the developed method. By comparing with some traditional methods, the obtained results reveal a close match that confirms both accuracy and correctness of the proposed method.

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Numerical Solutions of Fuzzy Fractional Delay Differential Equations

Cited by 4 publications

References 25 publications

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

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

Application of an Effective Method on the System of Nonlinear Fuzzy Integro-Differential Equations

Artificial neural network approach for solving fuzzy fractional order initial value problems under gH‐differentiability

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