Shifted Legendre Operational Matrix for Solving Fractional Order Lane–Emden Equation

Tripathi, Neeraj

doi:10.1007/s40009-018-0708-0

Cited by 1 publication

(1 citation statement)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The problem (1) was studied by using the Residual Power Series Method by Syam, M. (2018), Homotopy analysis method (HAM) by Huan et al (2017), Reproducing kernel Hilbert space method by Syam et al (2018), The fractional differential transformation (FDT) Rebenda and Smarda . (1978), Polynomial Least Squares Method by Caruntu et al (2019), Shifted Legendre Operational Matrix by Tripathi N. (2019), Chebyshev wavelets by Kazemi Nasab et al (2018), Orthonormal Bernoulli's polynomials by Sahu and Mallick. (2019), Orthonormal Bernstein polynomials by Abbas et al (2019).…”

Section: Introductionmentioning

confidence: 99%

A new operational matrix based on Boubaker polynomials for solving fractional Emden-Fowler problem

Bencheikh¹,

Chiter²

2022

Preprint

View full text Add to dashboard Cite

In this paper the singular Emden-Fowler equation of fractional order is introduced and a computational method is proposed for its numerical solution. For the approximation of the solutions we have used Boubaker polynomials and defined the formulation for its fractional derivative operational matrix. This tool was not used yet, however, this area has not found many practical applications yet, and here introduced for the first time. The operational matrix of the Caputo fractional derivative tool converts these problems to a system of algebraic equations whose solutions are simple and easy to compute. Numerical examples are examined to prove the validity and the effectiveness of the proposed method to find approximate and precise solutions.

show abstract