An accurate method for solving a singular second-order fractional Emden-Fowler problem

Muhammed I. Syam; Hm Jaradat; Marwan Alquran; Safwan Al-Shara’

doi:10.1186/s13662-018-1469-2

An accurate method for solving a singular second-order fractional Emden-Fowler problem

Muhammed I. Syam, Hm Jaradat, Marwan Alquran, Safwan Al-Shara’

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we study a singular second-order fractional Emden-Fowler problem. The reproducing kernel Hilbert space method (RKHSM) is employed to compute an approximation to the proposed problem. The construction of the reproducing kernel based on orthonormal shifted Legendre polynomials is presented. The validity of the RKHSM is ascertained by presenting several examples. We prove the existence of solution of the singular second-order fractional Emden-Fowler problem. The convergence of the approximate solution using the proposed method is investigated. The uniform convergence of the approximate solution to the exact solution is presented. Error estimation to the proposed method is proven. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems.

Original language	English
Article number	30
Journal	Advances in Difference Equations
Volume	2018
Issue number	1
DOIs	https://doi.org/10.1186/s13662-018-1469-2
Publication status	Published - Dec 1 2018

Keywords

nonlinear initial value problem
reproducing kernel Hilbert space method
singular second-order fractional Emden-Fowler problem

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1186/s13662-018-1469-2

Cite this

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abstract = "In this paper, we study a singular second-order fractional Emden-Fowler problem. The reproducing kernel Hilbert space method (RKHSM) is employed to compute an approximation to the proposed problem. The construction of the reproducing kernel based on orthonormal shifted Legendre polynomials is presented. The validity of the RKHSM is ascertained by presenting several examples. We prove the existence of solution of the singular second-order fractional Emden-Fowler problem. The convergence of the approximate solution using the proposed method is investigated. The uniform convergence of the approximate solution to the exact solution is presented. Error estimation to the proposed method is proven. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems.",

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AU - Syam, Muhammed I.

AU - Jaradat, Hm

AU - Alquran, Marwan

AU - Al-Shara’, Safwan

PY - 2018/12/1

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N2 - In this paper, we study a singular second-order fractional Emden-Fowler problem. The reproducing kernel Hilbert space method (RKHSM) is employed to compute an approximation to the proposed problem. The construction of the reproducing kernel based on orthonormal shifted Legendre polynomials is presented. The validity of the RKHSM is ascertained by presenting several examples. We prove the existence of solution of the singular second-order fractional Emden-Fowler problem. The convergence of the approximate solution using the proposed method is investigated. The uniform convergence of the approximate solution to the exact solution is presented. Error estimation to the proposed method is proven. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems.

AB - In this paper, we study a singular second-order fractional Emden-Fowler problem. The reproducing kernel Hilbert space method (RKHSM) is employed to compute an approximation to the proposed problem. The construction of the reproducing kernel based on orthonormal shifted Legendre polynomials is presented. The validity of the RKHSM is ascertained by presenting several examples. We prove the existence of solution of the singular second-order fractional Emden-Fowler problem. The convergence of the approximate solution using the proposed method is investigated. The uniform convergence of the approximate solution to the exact solution is presented. Error estimation to the proposed method is proven. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems.

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An accurate method for solving a singular second-order fractional Emden-Fowler problem

Abstract

Keywords

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