Non-Polynomial Collocation Spectral Scheme for Systems of Nonlinear Caputo–Hadamard Differential Equations-Reference-Cited by-同舟云学术

Non-Polynomial Collocation Spectral Scheme for Systems of Nonlinear Caputo–Hadamard Differential Equations

Published:2024-04-27 Issue:5 Volume:8 Page:262
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Zaky Mahmoud A.¹²^ORCID,Ameen Ibrahem G.³^ORCID,Babatin Mohammed¹^ORCID,Akgül Ali⁴⁵^ORCID,Hammad Magda⁶^ORCID,Lopes António M.⁷^ORCID

Affiliation:

1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia

2. Department of Applied Mathematics, Physics Research Institute, National Research Centre, Dokki, Cairo 12622, Egypt

3. Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt

4. Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Turkey

5. Department of Computer Science and Mathematics, Lebanese American University, Beirut 102, Lebanon

6. Department of Mathematics and Information Science, Faculty of Science, Beni-Suef University, Beni-Suef 62514, Egypt

7. LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

Abstract

In this paper, we provide a collocation spectral scheme for systems of nonlinear Caputo–Hadamard differential equations. Since the Caputo–Hadamard operators contain logarithmic kernels, their solutions can not be well approximated using the usual spectral methods that are classical polynomial-based schemes. Hence, we construct a non-polynomial spectral collocation scheme, describe its effective implementation, and derive its convergence analysis in both L2 and L∞. In addition, we provide numerical results to support our theoretical analysis.

Funder

Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University

Publisher

MDPI AG

Link

https://www.mdpi.com/2504-3110/8/5/262/pdf

Reference20 articles.

1. Hilfer, R. (2000). Applications of Fractional Calculus in Physics, World Scientific.

2. Yang, Y., and Zhang, H.H. (2022). Fractional Calculus with Its Applications in Engineering and Technology, Springer Nature.

3. Essai sur l’étude des fonctions données par leur développement de Taylor;Hadamard;J. Math. Pures Appl.,1892

4. Stochastic model for ultraslow diffusion;Meerschaert;Stoch. Process. Their Appl.,2006

5. Distributed order calculus and equations of ultraslow diffusion;Kochubei;J. Math. Anal. Appl.,2008

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