2018
DOI: 10.1186/s13662-018-1924-0
|View full text |Cite
|
Sign up to set email alerts
|

A method for fractional Volterra integro-differential equations by Laguerre polynomials

Abstract: The main purpose of this study is to present an approximation method based on the Laguerre polynomials for fractional linear Volterra integro-differential equations. This method transforms the integro-differential equation to a system of linear algebraic equations by using the collocation points. In addition, the matrix relation for Caputo fractional derivatives of Laguerre polynomials is also obtained. Besides, some examples are presented to illustrate the accuracy of the method and the results are discussed.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3

Citation Types

0
3
0

Year Published

2021
2021
2024
2024

Publication Types

Select...
8

Relationship

0
8

Authors

Journals

citations
Cited by 13 publications
(3 citation statements)
references
References 54 publications
0
3
0
Order By: Relevance
“…Different approaches have been studied to solve FIE. Ghosh [8] employed Katugampola fractional operator to investigate analytical approach for the fractional-order Hepatitis B model, Ghosh & Kumar [9] investigated the accuracy of fractional Covid-19 model via spectral collocation method, Jani et al [10] investigated the accuracy of numerical solution of FIE with non-local conditions using Bernstein polynomials, Zaky [11] proposed improved tau method to investigate the accuracy of multi-dimensional fractional Rayleigh-Stokes problem, Wang & Zhu [12] proposed Euler wavelet operational matrix method for solving non-linear Volterra integro-differential equations, Huang et al [13] tested the effectiveness of Taylor expansion method on the solution of FIE, Bayram & Das ¸cioglu [14,15] investigated the accuracy of fractional linear Volterra-Fredholm IDEs via Laguerre polynomials as an approximation, Mittal & Nigam [16] investigated the accuracy of Adomian decomposition method (ADM) in the solution of FIE. Convergence of Jacobi spectral collocation method was investigated in the solution of FIE by Huang et al [17,18], FIE with weakly singular kernel was studied using legendre wavelets method by Yi et al [19], spline collocation method was used to solve fractional weakly singular IDEs by Pedas et al [20].…”
Section: Introductionmentioning
confidence: 99%
“…Different approaches have been studied to solve FIE. Ghosh [8] employed Katugampola fractional operator to investigate analytical approach for the fractional-order Hepatitis B model, Ghosh & Kumar [9] investigated the accuracy of fractional Covid-19 model via spectral collocation method, Jani et al [10] investigated the accuracy of numerical solution of FIE with non-local conditions using Bernstein polynomials, Zaky [11] proposed improved tau method to investigate the accuracy of multi-dimensional fractional Rayleigh-Stokes problem, Wang & Zhu [12] proposed Euler wavelet operational matrix method for solving non-linear Volterra integro-differential equations, Huang et al [13] tested the effectiveness of Taylor expansion method on the solution of FIE, Bayram & Das ¸cioglu [14,15] investigated the accuracy of fractional linear Volterra-Fredholm IDEs via Laguerre polynomials as an approximation, Mittal & Nigam [16] investigated the accuracy of Adomian decomposition method (ADM) in the solution of FIE. Convergence of Jacobi spectral collocation method was investigated in the solution of FIE by Huang et al [17,18], FIE with weakly singular kernel was studied using legendre wavelets method by Yi et al [19], spline collocation method was used to solve fractional weakly singular IDEs by Pedas et al [20].…”
Section: Introductionmentioning
confidence: 99%
“…Fractional integro-differential equations are sometimes difficult to solve analytically, requiring the construction of effective approximation solutions. The Jacobi spectral method [20], Runge Kutta method [24], Chebyshev collocation method [3], Laplace Power Series Method [1], rationalized Haar functions method [15], Galerkin methods with hybrid functions [14] and Laguerre collocation method [5] are just a few of the numerical techniques that have been used to solve such equations.…”
Section: Introductionmentioning
confidence: 99%
“…Preliminarily, Bayram et al [12] have applied the Sinc-collocation method, and Daşcıoğlu et al [13] have used a collocation method based upon the Laguerre polynomials to attain the solutions of the linear fractional IDEs in the conformable sense. This method mentioned in [13] is an improvement of the method that had been used for the solutions of the linear Caputo fractional IDEs of the Volterra type [14] and Caputo fractional linear IDEs of the Fredholm type [15]. However, for the conformable fractional Fredholm IDEs, there has not been a method in the literature in the sense of Chebyshev polynomials.…”
Section: Introductionmentioning
confidence: 99%