A new efficient method using Fibonacci polynomials for solving of first-order fuzzy Fredholm–Volterra integro-differential equations

Seifi, Ali Reza; Lotfi, Taher; Allahviranloo, Tofigh

doi:10.1007/s00500-019-04031-1

Cited by 9 publications

(5 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Fibonacci polynomials are defined by a recurrence relation 17–26

F_{n} false(t false) = ({, \begin{matrix} left leftarray \\ array 0, & array n = 0, \\ array 1, & array n = 1, \\ array t F_{n - 1} (t) + F_{n - 2} (t), & array n \geq 2 . \end{matrix})

…”

Section: Required Toolsmentioning

confidence: 99%

“…The Fibonacci polynomials are defined by a recurrence relation [17][18][19][20][21][22][23][24][25][26] F n (t) =…”

Section: Fibonacci Polynomialsmentioning

confidence: 99%

“…Mirzaee and Hoseini 22,23 provided a method based on Fibonacci polynomials to introduce an approximate solution of the high‐order linear system of Fredholm integrodifferential equations under the mixed conditions with variable coefficients and singularly perturbed differential–difference equations with mixed shifts. Seifi et al 24 proposed a numerical approach based on Fibonacci polynomials for solving first‐order fuzzy Fredholm–Volterra integrodifferential equations of the second kind. Abd‐Elhameed and Youssri 25 presented a numerical method based on the generalized Fibonacci polynomials for a certain coupled system of fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal study on fractional fascioliasis disease model based on generalized Fibonacci polynomials

Avazzadeh

Hassani

Agarwal

et al. 2023

Math Methods in App Sciences

View full text Add to dashboard Cite

Funding informationThere are no funders to report for this submission.Fascioliasis is a liver fluke disease in which food and water are the transmitting agents. The disease is caused by a genus of Fasciola, parasitic Trematoda. The genus Fasciola includes two species of Fasciola gigantica and Fasciola hepatica.The study of this disease is of particular importance as the infected cases are globally growing, especially in endemic areas. In this paper, a fractional-order mathematical model is presented for fascioliasis disease. The optimization method is an effective choice in solving mathematical models of epidemic diseases. The study aims at presenting a new set of generalized Fibonacci polynomials as basic functions and some innovative operational matrices of derivatives in the Caputo sense to solve the fascioliasis disease model. The numerical experiments reveal better results and simulations show effectiveness of the presented method.

show abstract

“…The Fibonacci polynomials are defined by a recurrence relation 17–26

F_{n} false(t false) = ({, \begin{matrix} left leftarray \\ array 0, & array n = 0, \\ array 1, & array n = 1, \\ array t F_{n - 1} (t) + F_{n - 2} (t), & array n \geq 2 . \end{matrix})

…”

Section: Required Toolsmentioning

confidence: 99%

“…The Fibonacci polynomials are defined by a recurrence relation [17][18][19][20][21][22][23][24][25][26] F n (t) =…”

Section: Fibonacci Polynomialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal study on fractional fascioliasis disease model based on generalized Fibonacci polynomials

Avazzadeh

Hassani

Agarwal

et al. 2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…The higher order FDEs and FPDEs have been excluded in this survey. Furthermore, there are some other types of uncertain differential equations such as random fuzzy differential equations [213]- [215], fuzzy integro differential equations [216], [217], and fuzzy fractional integro differential equations [218], [219] which have not been included in this paper. Note 3: Interval-valued differential equations may be viewed as a special case of fuzzy differential equations where the uncertainty is considered as an interval in which each member has a full grade of membership to the interval.…”

Section: Applications Of Fdesmentioning

confidence: 99%

A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

2021

IEEE Access

View full text Add to dashboard Cite

Since the term "Fuzzy differential equations" (FDEs) emerged in the literature in 1978, prevailing research effort has been dedicated not only to the development of the concepts concerning the topic, but also to its potential applications. This paper presents a chronological survey on fuzzy differential equations of integer and fractional orders. Attention is concentrated on the FDEs in which a definition of fuzzy derivative of a fuzzy number-valued function has been taken into account. The chronological rationale behind considering FDEs under each concept of fuzzy derivative is highlighted. The pros and cons of each approach dealing with FDEs are also discussed. Moreover, some of the proposed FDEs applications and methods for solving them are investigated. Finally, some of the future perspectives and challenges of fuzzy differential equations are discussed based on our personal view point.

show abstract

“…The CSIEs have been solved via various numerical techniques such as using orthogonal Legendre polynomial [6], Lagrangian interpolation with Gauss-Jacobi mechanical quadrature [8], spline method [12,13], Galerkin technique [14], collocation method [15][16][17], application of Jacobi polynomials [18], using Chebyshev polynomials of the second kind [19], quadrature formula [20][21][22], reproducing kernel Hilbert space method [23,24], and other schemes [25][26][27]. Recently, several types of operational matrix methods with truncated series have been proposed for solving the integral and integro-differential equations (see [16,28]).…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of certain Cauchy singular integral equations using a collocation scheme

Seifi

2020

Adv Differ Equ

View full text Add to dashboard Cite

The present study is devoted to developing a computational collocation technique for solving the Cauchy singular integral equation of the second kind (CSIE-2). Although, several studies have investigated the numerical approximation solution of CSIEs, the strong singularity and accuracy of the numerical methods are still two important challenges for these integral equations. In this paper, we focus on the smooth transformation and implementation of Bessel basis polynomials (BBP). The reduction of the CSIEs-2 into a system of algebraic equations with the Gauss–Legendre collocation points simplifies this technique. The technique of performing numerical approximation of the solution is well presented and illustrated in the matrix form. Also, the convergence and error bound associated with the scheme are established. Finally, several experiments show the reliability and numerical efficiency of the proposed scheme in comparison with other methods.

show abstract

A new efficient method using Fibonacci polynomials for solving of first-order fuzzy Fredholm–Volterra integro-differential equations

Cited by 9 publications

References 36 publications

Optimal study on fractional fascioliasis disease model based on generalized Fibonacci polynomials

Optimal study on fractional fascioliasis disease model based on generalized Fibonacci polynomials

A Review on Fuzzy Differential Equations

Numerical solution of certain Cauchy singular integral equations using a collocation scheme

Contact Info

Product

Resources

About