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Dergiler / Sigma Journal of Engineering and Natural Sciences / 2026 / Volume: 42 Issue: 4

Operational matrix for multi-order fractional differential equations with hermite polynomials

Hatice Yalman Koşunalp(Department of Accounting and Tax, Gonen Vocational School, Bandırma Onyedi Eylul University, Balıkesir, 10200, Türkiye)0000-0001-6313-862X
Mustafa Gülsu(Department of Mathematics, Faculty of Science, Mugla Sitki Kocman University, Mugla, 48000, Türkiye)0000-0001-6139-0266
Sayfa
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Yayın Tarihi
2024-08-01
DOI
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Numerical results indicate that the proposed method provides a high degree of accuracy to solve the linear multi-order FDEs.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this article, a new operational matrix of fractional integration of Hermite polynomials is derived to solve multi-order linear fractional differential equations (FDEs) with spectral tau approach.
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Temel Bulgular & Veri:We firstly convert the FDEs into an integrated-form through multiple fractional integration in association with the Riemann-Liouville sense.
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Sonuç & Katkı:Numerical results indicate that the proposed method provides a high degree of accuracy to solve the linear multi-order FDEs.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fractional Differential Equations · Orthogonal Polynomials · Operational Matrix

Abstract

In this article, a new operational matrix of fractional integration of Hermite polynomials is derived to solve multi-order linear fractional differential equations (FDEs) with spectral tau approach. We firstly convert the FDEs into an integrated-form through multiple fractional integration in association with the Riemann-Liouville sense. This integral equation is then formulated as an algebraic equation system with Hermite polynomials. Finally, linear multi-order FDEs with initial conditions are solved with this method. We present exact and approximated solutions for a number of representative examples. Numerical results indicate that the proposed method provides a high degree of accuracy to solve the linear multi-order FDEs.

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Bu Makaleye Atıf Yap

Koşunalp, H. Y., Gülsu, M. (2024). Operational matrix for multi-order fractional differential equations with hermite polynomials. Sigma Journal of Engineering and Natural Sciences, Volume: 42 Issue: 4. https://ajindex.com/articles/1632232

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