Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations

Dilek Varol; Ayşegül Daşcıoğlu

doi:10.32323/ujma.1390222

EN

Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations

Abstract

This paper discusses the linear fractional Fredholm-Volterra integro-differential equations (IDEs) considered in the Caputo sense. For this purpose, Laguerre polynomials have been used to construct an approximation method to obtain the solutions of the linear fractional Fredholm-Volterra IDEs. By this approximation method, the IDE has been transformed into a linear algebraic equation system using appropriate collocation points. In addition, a novel and exact matrix expression for the Caputo fractional derivatives of Laguerre polynomials and an associated explicit matrix formulation has been established for the first time in the literature. Furthermore, a comparison between the results of the proposed method and those of methods in the literature has been provided by implementing the method in numerous examples.

Keywords

Caputo fractional derivatives, Fredholm-Volterra integro-differential equations, Laguerre polynomials

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations

Journal Section

Research Article

Authors

Dilek Varol
0000-0002-5158-5614
Türkiye

Ayşegül Daşcıoğlu ^*
0000-0001-8931-6930
Türkiye

Early Pub Date

February 15, 2024

Publication Date

March 18, 2024

Submission Date

November 13, 2023

Acceptance Date

February 6, 2024

Published in Issue

Year 2024 Volume: 7 Number: 1

DOI

https://doi.org/10.32323/ujma.1390222

IZ

https://izlik.org/JA39ZG48FL

APA

Varol, D., & Daşcıoğlu, A. (2024). Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations. Universal Journal of Mathematics and Applications, 7(1), 38-45. https://doi.org/10.32323/ujma.1390222

AMA

1.Varol D, Daşcıoğlu A. Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations. Univ. J. Math. Appl. 2024;7(1):38-45. doi:10.32323/ujma.1390222

Chicago

Varol, Dilek, and Ayşegül Daşcıoğlu. 2024. “Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations”. Universal Journal of Mathematics and Applications 7 (1): 38-45. https://doi.org/10.32323/ujma.1390222.

EndNote

Varol D, Daşcıoğlu A (March 1, 2024) Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations. Universal Journal of Mathematics and Applications 7 1 38–45.

IEEE

[1]D. Varol and A. Daşcıoğlu, “Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations”, Univ. J. Math. Appl., vol. 7, no. 1, pp. 38–45, Mar. 2024, doi: 10.32323/ujma.1390222.

ISNAD

Varol, Dilek - Daşcıoğlu, Ayşegül. “Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations”. Universal Journal of Mathematics and Applications 7/1 (March 1, 2024): 38-45. https://doi.org/10.32323/ujma.1390222.

JAMA

1.Varol D, Daşcıoğlu A. Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations. Univ. J. Math. Appl. 2024;7:38–45.

MLA

Varol, Dilek, and Ayşegül Daşcıoğlu. “Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations”. Universal Journal of Mathematics and Applications, vol. 7, no. 1, Mar. 2024, pp. 38-45, doi:10.32323/ujma.1390222.

Vancouver

1.Dilek Varol, Ayşegül Daşcıoğlu. Laguerre Collocation Approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations. Univ. J. Math. Appl. 2024 Mar. 1;7(1):38-45. doi:10.32323/ujma.1390222