Innovative Method for Computing Approximate Solutions of Non-Homogeneous Wave Equations with Generalized Fractional Derivatives
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Published:2023-11-09
Issue:
Volume:
Page:1026-1047
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ISSN:2705-1056
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Container-title:Contemporary Mathematics
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language:
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Short-container-title:Contemp. Math.
Author:
Hashemi Mir SajjadORCID,
Mirzazadeh Mohammad,
Baleanu Dumitru
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.
Publisher
Universal Wiser Publisher Pte. Ltd
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics