Innovative Method for Computing Approximate Solutions of Non-Homogeneous Wave Equations with Generalized Fractional Derivatives

Authors

  • Mir Sajjad Hashemi Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran https://orcid.org/0000-0002-5529-3125
  • Mohammad Mirzazadeh Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891- 63157 Rudsar-Vajargah, Iran
  • Dumitru Baleanu Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

DOI:

https://doi.org/10.37256/cm.4420233593

Keywords:

shifted Chebyshev polynomial, wave equation, generalized Caputo fractional derivative, irregular domain

Abstract

In this work, a well-known non-homogeneous wave equation with temporal fractional derivative is approximately investigated. A recently defined generalized non-local fractional derivative is utilized as the fractional operator. A novel technique is proposed to approximate the solutions of wave equation with generalized fractional derivative. The proposed method is based on the shifted Chebyshev polynomials and a combination of collocation and residual function methods. Theoretical analysis of the convergence of the proposed method is performed. Approximate solutions are derived in both rectangular and non-rectangular (general) domains.

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Published

2023-11-09

How to Cite

1.
Hashemi MS, Mirzazadeh M, Baleanu D. Innovative Method for Computing Approximate Solutions of Non-Homogeneous Wave Equations with Generalized Fractional Derivatives. Contemp. Math. [Internet]. 2023 Nov. 9 [cited 2024 May 28];4(4):1026-47. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3593

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