Nth-order Fuzzy Differential Equations Under Generalized Differentiability

Salahshour, Soheil

doi:10.5899/2011/jfsva-00043

Cited by 10 publications

(4 citation statements)

References 23 publications

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“…In this section, we formulate the trial and error function of ChNN method to approximate nonlinear nth order FDEs. Analytical and numerical investigations of nth order FDEs are accomplished by various authors, for instance, Jayakumar et al [10] used Runge-Kutta method of order five to numerically solve nth order FDEs, Salahshour [25] proposed an integral form to examine analytical solutions of these equations, Ahmady [26] proposed piecewise approximation method to discuss the solutions of nth order FDEs etc. Comparatively, ChNN for its less computational complexity, executes the appropriate analytical approximations more rapidly.…”

Section: Formulation Of Chnn For Nonlinear Nth Order Fuzzy Differentimentioning

confidence: 99%

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

Ara

Razzaq

Khan

2018

Annals of West University of Timisoara - Mathematics and Computer Science

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Bearing in mind the considerable importance of fuzzy differential equations (FDEs) in different fields of science and engineering, in this paper, nonlinear nth order FDEs are approximated, heuristically. The analysis is carried out on using Chebyshev neural network (ChNN), which is a type of single layer functional link artificial neural network (FLANN). Besides, explication of generalized Hukuhara differentiability (gH-differentiability) is also added for the nth order differentiability of fuzzy-valued functions. Moreover, general formulation of the structure of ChNN for the governing problem is described and assessed on some examples of nonlinear FDEs. In addition, comparison analysis of the proposed method with Runge-Kutta method is added and also portrayed the error bars that clarify the feasibility of attained solutions and validity of the method.

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Section: Formulation Of Chnn For Nonlinear Nth Order Fuzzy Differentimentioning

confidence: 99%

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

Ara

Razzaq

Khan

2018

Annals of West University of Timisoara - Mathematics and Computer Science

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“…Definition 2.9 (Salahshour, 2011). Define the mapping f 0 : I !Ẽ and y 0 2 I, where I 2 ½t 0 ; T. We say thatf 0 is Hukuhara differentiable t 2Ẽ, if there exists an element ½f ðnÞ r 2Ẽ such that for all h > 0 sufficiently small (near to 0), existf ðnÀ1Þ ðy 0 þ h; rÞ€f ðnÀ1Þ ðy 0 ; rÞ, andf ðnÀ1Þ ðy 0 ; rÞ€f ðnÀ1Þ ðy 0 À h; rÞ and the limits are taken in the metric ðẼ; DÞ…”

Section: Preliminariesmentioning

confidence: 99%

Optimal homotopy asymptotic method for solvingnth order linear fuzzy initial value problems

Jameel

Ismail

Mabood

2016

Journal of the Association of Arab Universities for Basic and A

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In this paper the optimal homotopy asymptotic method (OHAM) is employed to obtain approximate analytical solution of nth order ðn P 2Þ linear fuzzy initial value problems (FIVPs). The convergence theorem of this method in fuzzy case is presented and proved. This method provides us with a convenient way to control the convergence of approximation series. The method is tested on nth linear FIVPs and comparisons of the exact solution that were made with numerical results showed the effectiveness and accuracy of this method.

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“…Feuring [3] etc. However earlier considered fuzzy differential equations used fuzzy Hukuhara derivative [9,12,13,15] and generalized derivative [1,2,5,19].…”

Section: Introductionmentioning

confidence: 99%