Operational matrix approach for solving variable-order fractional integro-differential equations

Praveen Agarwal; A. A. El-Sayed

doi:10.1016/B978-0-32-390953-2.00025-6

Operational matrix approach for solving variable-order fractional integro-differential equations

Praveen Agarwal
, A. A. El-Sayed

Nonlinear Dynamic Research Centre (NDRC)

International College of Engineering
People's Friendship University of Russia
Al-Fayoum University
University of Technology and Applied Sciences-AlRustaq

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

In this paper, we use shifted fourth-kind Chebyshev polynomials to construct the operational matrix technique for numerical solution of variable-order fractional integro-differential equations (VO-FIDEs). We construct both fractional differential and integral operational matrices. These matrices coincide with the Chebyshev collocation method used to transform the main problem into an algebraic system of equations. By solving this system of equations we get the numerical solution of the original equation. Finally, we give several numerical examples to show that the numerical technique is applicable and computationally efficient.

Original language	English
Title of host publication	Fractional Order Systems and Applications in Engineering
Publisher	Elsevier
Pages	301-317
Number of pages	17
ISBN (Electronic)	9780323909532
ISBN (Print)	9780323909549
DOIs	https://doi.org/10.1016/B978-0-32-390953-2.00025-6
State	Published - 1 Jan 2022

Keywords

Fourth-kind Chebyshev polynomials
Riemann-Liouville integral operator
Spectral collocation method
Variable-order Caputo differential operator
Variable-order fractional integro-differential equations

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10.1016/B978-0-32-390953-2.00025-6

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title = "Operational matrix approach for solving variable-order fractional integro-differential equations",

abstract = "In this paper, we use shifted fourth-kind Chebyshev polynomials to construct the operational matrix technique for numerical solution of variable-order fractional integro-differential equations (VO-FIDEs). We construct both fractional differential and integral operational matrices. These matrices coincide with the Chebyshev collocation method used to transform the main problem into an algebraic system of equations. By solving this system of equations we get the numerical solution of the original equation. Finally, we give several numerical examples to show that the numerical technique is applicable and computationally efficient.",

keywords = "Fourth-kind Chebyshev polynomials, Riemann-Liouville integral operator, Spectral collocation method, Variable-order Caputo differential operator, Variable-order fractional integro-differential equations",

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T1 - Operational matrix approach for solving variable-order fractional integro-differential equations

AU - Agarwal, Praveen

AU - El-Sayed, A. A.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - In this paper, we use shifted fourth-kind Chebyshev polynomials to construct the operational matrix technique for numerical solution of variable-order fractional integro-differential equations (VO-FIDEs). We construct both fractional differential and integral operational matrices. These matrices coincide with the Chebyshev collocation method used to transform the main problem into an algebraic system of equations. By solving this system of equations we get the numerical solution of the original equation. Finally, we give several numerical examples to show that the numerical technique is applicable and computationally efficient.

AB - In this paper, we use shifted fourth-kind Chebyshev polynomials to construct the operational matrix technique for numerical solution of variable-order fractional integro-differential equations (VO-FIDEs). We construct both fractional differential and integral operational matrices. These matrices coincide with the Chebyshev collocation method used to transform the main problem into an algebraic system of equations. By solving this system of equations we get the numerical solution of the original equation. Finally, we give several numerical examples to show that the numerical technique is applicable and computationally efficient.

KW - Fourth-kind Chebyshev polynomials

KW - Riemann-Liouville integral operator

KW - Spectral collocation method

KW - Variable-order Caputo differential operator

KW - Variable-order fractional integro-differential equations

UR - https://www.scopus.com/pages/publications/85150147717

U2 - 10.1016/B978-0-32-390953-2.00025-6

DO - 10.1016/B978-0-32-390953-2.00025-6

M3 - Chapter

AN - SCOPUS:85150147717

SN - 9780323909549

SP - 301

EP - 317

BT - Fractional Order Systems and Applications in Engineering

PB - Elsevier

ER -

Operational matrix approach for solving variable-order fractional integro-differential equations

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Keywords

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