An Efficient Method for Solving Singularly Perturbed Riccati Equation with Fractional Order

Muhammed I. Syam; Alaa Haroun; Marwa Al Refai; M. Naim Anwar

doi:10.1007/s40819-017-0474-6

An Efficient Method for Solving Singularly Perturbed Riccati Equation with Fractional Order

Muhammed I. Syam, Alaa Haroun, Marwa Al Refai, M. Naim Anwar

Department of Mathematical Sciences

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

3 Citations (Scopus)

Abstract

In this paper, we study a class of singularly perturbed Riccati equation with fractional order. We divide the problem into three problems. The first problem is the reduced problem when ϵ= 0. The second and third problems are fractional Riccati problem. The results show that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. Numerical results are presented.

Original language	English
Article number	32
Journal	International Journal of Applied and Computational Mathematics
Volume	4
Issue number	1
DOIs	https://doi.org/10.1007/s40819-017-0474-6
Publication status	Published - Feb 1 2018

Keywords

Caputo fractional derivative
Nonlinear initial value problem
Singularly perturbed Riccati equation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s40819-017-0474-6

Cite this

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title = "An Efficient Method for Solving Singularly Perturbed Riccati Equation with Fractional Order",

abstract = "In this paper, we study a class of singularly perturbed Riccati equation with fractional order. We divide the problem into three problems. The first problem is the reduced problem when ϵ= 0. The second and third problems are fractional Riccati problem. The results show that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. Numerical results are presented.",

keywords = "Caputo fractional derivative, Nonlinear initial value problem, Singularly perturbed Riccati equation",

author = "Syam, {Muhammed I.} and Alaa Haroun and {Al Refai}, Marwa and Anwar, {M. Naim}",

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AU - Syam, Muhammed I.

AU - Haroun, Alaa

AU - Al Refai, Marwa

AU - Anwar, M. Naim

N1 - Funding Information: Acknowledgements The authors would like to express their sincere appreciation to United Arab Emirates University for the financial support of Grant No. G00002406. In addition, The authors would like to express their appreciation for the valuable comments of the reviewers. Publisher Copyright: © 2017, Springer (India) Private Ltd., part of Springer Nature.

PY - 2018/2/1

Y1 - 2018/2/1

N2 - In this paper, we study a class of singularly perturbed Riccati equation with fractional order. We divide the problem into three problems. The first problem is the reduced problem when ϵ= 0. The second and third problems are fractional Riccati problem. The results show that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. Numerical results are presented.

AB - In this paper, we study a class of singularly perturbed Riccati equation with fractional order. We divide the problem into three problems. The first problem is the reduced problem when ϵ= 0. The second and third problems are fractional Riccati problem. The results show that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. Numerical results are presented.

KW - Caputo fractional derivative

KW - Nonlinear initial value problem

KW - Singularly perturbed Riccati equation

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An Efficient Method for Solving Singularly Perturbed Riccati Equation with Fractional Order

Abstract

Keywords

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