Analytical and numerical solutions of fuzzy differential equations

Ahmad, Muhammad Zaini; Hasan, Mohammad Khatim; Baets, Bernard De

doi:10.1016/j.ins.2013.02.026

Cited by 68 publications

(37 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since f is fuzzy-valued function, therefore parametric representation of Eq. (19) will be, for ≤ r ≤ : (22) .…”

Section: Fuzzy Sumudu Transformationmentioning

confidence: 99%

“…Fuzzy theory plays an important role in modeling dynamical systems under uncertainty. Fuzzy linear di erential equations are one of the simplest fuzzy di erential models which have signi cant importance in many applications [18][19][20][21][22][23][24][25][26]. Here fuzzy di erential equations are considered under generalized Hukuhara di erentiability.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the solution of fuzzy differential equations by Fuzzy Sumudu Transform

Khan

Razzaq

Ayyaz

2015

Nonlinear Engineering

View full text Add to dashboard Cite

In this paper, Sumudu transform is advanced and designed for the solution of linear di erential models with uncertainty. For this purpose, Sumudu transform is coupled with fuzzy theory and all its fundamental properties are formalized in fuzzy sense. At last, to demonstrate the accuracy of this approach, fuzzy Sumudu transform is employed to some examples of fuzzy linear di erential equations considered under generalized Hdi erentiability and analytical solutions are obtained eciently.

show abstract

“…Since f is fuzzy-valued function, therefore parametric representation of Eq. (19) will be, for ≤ r ≤ : (22) .…”

Section: Fuzzy Sumudu Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the solution of fuzzy differential equations by Fuzzy Sumudu Transform

Khan

Razzaq

Ayyaz

2015

Nonlinear Engineering

View full text Add to dashboard Cite

show abstract

“…The reader is asked to refer to Abu , Abu Arqub et al (2013a, b), Ahmad et al (2013), Allahviranloo et al (2009a, b), Effati and Pakdaman (2010), Khastan and Ivaz (2009), Khastan et al (2011), Ma et al (1999), Mosleh (2013), and Palligkinis et al (2009) to know more details about these methods, including their kinds and history, their modification and conditions for use, their scientific applications, their importance and characteristics, and their relationship including the differences.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method

et al. 2015

View full text Add to dashboard Cite

Modeling of uncertainty differential equations is very important issue in applied sciences and engineering, while the natural way to model such dynamical systems is to use fuzzy differential equations. In this paper, we present a new method for solving fuzzy differential equations based on the reproducing kernel theory under strongly generalized differentiability. The analytic and approximate solutions are given with series form in terms of their parametric form inThe method used in this paper has several advantages; first, it is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical, physical, and engineering problems; second, it is accurate, needs less effort to achieve the results, and is developed especially for the nonlinear cases; third, in the proposed method, it is possible to pick any point in the interval of integration and as well the approximate solutions and their derivatives will be applicable; fourth, the method does not require discretization of the variables, and it is not effected by computation round off errors and one is not faced with necessity of large computer memory and time. Results presented in this paper show potentiality, generality, and superiority of our method as compared with other well-known methods.

show abstract

“…Allahviranloo et al [14] applied AdamsBashforth, Adams-Moulton, and predictor-corrector methods to solve fuzzy ordinary differential equations. Ahmad et al [15] and predictor-corrector methods are iterative for which the step size should be fixed before initiating the computation. After obtaining the solution, if one needs to know the solution in between of any steps, the process needs to be repeated from primary stage.…”

Section: Introductionmentioning

confidence: 99%

A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation

Khan

Shaikh

Raja

et al. 2016

Journal of Applied Mathematics, Statistics and Informatics

View full text Add to dashboard Cite

In this article, Legendre simulated annealing, neural network (LSANN) is designed for fuzzy fractional order differential equations, which is employed on fractional fuzzy initial value problem (FFIVP) with triangular condition. Here, Legendre polynomials are used to modify the structure of neural networks with a Taylor series approximation of the tangent hyperbolic as activation function while the network adaptive coefficients are trained in the procedure of simulated annealing to optimize the residual error. The computational results are depicted in terms of numerical values to compare them with previous results.

show abstract

Analytical and numerical solutions of fuzzy differential equations

Cited by 68 publications

References 38 publications

On the solution of fuzzy differential equations by Fuzzy Sumudu Transform

On the solution of fuzzy differential equations by Fuzzy Sumudu Transform

Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method

A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation

Contact Info

Product

Resources

About