Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order

Bothayna S.H. Kashkari; Muhammed I. Syam

doi:10.1016/j.amc.2016.06.003

Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order

Bothayna S.H. Kashkari
, Muhammed I. Syam

Department of Mathematical Sciences

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

60 Citations (Scopus)

Abstract

This paper is devoted to both theoretical and numerical study of Riccati equation with fractional order. A formulation to the fractional-order Legendre operational matrix of fractional integration is constructed. Existence and uniqueness results for the considered problem are provided and proved. The fractional derivative is described in the Caputo sense. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.

Original language	English
Pages (from-to)	281-291
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	290
DOIs	https://doi.org/10.1016/j.amc.2016.06.003
Publication status	Published - Nov 1 2016

Keywords

Fractional-order Legendre function
Operational matrix of fractional integration
Riccati equation with fractional order

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2016.06.003

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abstract = "This paper is devoted to both theoretical and numerical study of Riccati equation with fractional order. A formulation to the fractional-order Legendre operational matrix of fractional integration is constructed. Existence and uniqueness results for the considered problem are provided and proved. The fractional derivative is described in the Caputo sense. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.",

keywords = "Fractional-order Legendre function, Operational matrix of fractional integration, Riccati equation with fractional order",

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doi = "10.1016/j.amc.2016.06.003",

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AU - Kashkari, Bothayna S.H.

AU - Syam, Muhammed I.

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Y1 - 2016/11/1

N2 - This paper is devoted to both theoretical and numerical study of Riccati equation with fractional order. A formulation to the fractional-order Legendre operational matrix of fractional integration is constructed. Existence and uniqueness results for the considered problem are provided and proved. The fractional derivative is described in the Caputo sense. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.

AB - This paper is devoted to both theoretical and numerical study of Riccati equation with fractional order. A formulation to the fractional-order Legendre operational matrix of fractional integration is constructed. Existence and uniqueness results for the considered problem are provided and proved. The fractional derivative is described in the Caputo sense. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.

KW - Fractional-order Legendre function

KW - Operational matrix of fractional integration

KW - Riccati equation with fractional order

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JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order

Abstract

Keywords

ASJC Scopus subject areas

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