Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets

Somayeh Nemati; Anas Al-haboobi

doi:10.32323/ujma.427381

EN

Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets

Abstract

In this work, we propose a numerical method based on the generalized sine-cosine wavelets for solving multi-order fractional differential equations. After introducing generalized sine-cosine wavelets, the operational matrix of Riemann-Liouville fractional integration is constructed using the properties of the block-pulse functions. The fractional derivative in the problem is considered in the Caputo sense. This method reduces the considered problem to the problem of solving a system of nonlinear algebraic equations. Finally, some examples are included to demonstrate the applicability of the new approach.

Keywords

Generalized sine-cosine wavelet,Operational matrix of fractional integration,Multi-order fractional differential equations,Block-pulse functions,Operational matrix of fractional integration

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Somayeh Nemati ^*
Iran

Anas Al-haboobi This is me
Iran

Publication Date

December 20, 2018

Submission Date

May 26, 2018

Acceptance Date

October 26, 2018

Published in Issue

Year 2018 Volume: 1 Number: 4

DOI

https://doi.org/10.32323/ujma.427381

IZ

https://izlik.org/JA79ES52DU

APA

Nemati, S., & Al-haboobi, A. (2018). Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets. Universal Journal of Mathematics and Applications, 1(4), 215-225. https://doi.org/10.32323/ujma.427381

AMA

1.Nemati S, Al-haboobi A. Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets. Univ. J. Math. Appl. 2018;1(4):215-225. doi:10.32323/ujma.427381

Chicago

Nemati, Somayeh, and Anas Al-haboobi. 2018. “Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets”. Universal Journal of Mathematics and Applications 1 (4): 215-25. https://doi.org/10.32323/ujma.427381.

EndNote

Nemati S, Al-haboobi A (December 1, 2018) Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets. Universal Journal of Mathematics and Applications 1 4 215–225.

IEEE

[1]S. Nemati and A. Al-haboobi, “Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets”, Univ. J. Math. Appl., vol. 1, no. 4, pp. 215–225, Dec. 2018, doi: 10.32323/ujma.427381.

ISNAD

Nemati, Somayeh - Al-haboobi, Anas. “Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets”. Universal Journal of Mathematics and Applications 1/4 (December 1, 2018): 215-225. https://doi.org/10.32323/ujma.427381.

JAMA

1.Nemati S, Al-haboobi A. Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets. Univ. J. Math. Appl. 2018;1:215–225.

MLA

Nemati, Somayeh, and Anas Al-haboobi. “Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets”. Universal Journal of Mathematics and Applications, vol. 1, no. 4, Dec. 2018, pp. 215-2, doi:10.32323/ujma.427381.

Vancouver

1.Somayeh Nemati, Anas Al-haboobi. Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets. Univ. J. Math. Appl. 2018 Dec. 1;1(4):215-2. doi:10.32323/ujma.427381

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https://doi.org/10.1016/j.padiff.2025.101131

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Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets

Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets

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Keywords

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