Spectral algorithm for fractional BVPs via novel modified Chebyshev polynomials fractional derivatives
DOI: https://doi.org/10.3846/mma.2025.22745Abstract
This paper introduces a spectral algorithm tailored for solving fractional boundary value problems (BVPs) using the fractional derivatives of modified Chebyshev polynomials. Specifically, it addresses linear and non-linear BVPs and Bratu equations in one dimension via spectral methods. The approach employs basis functions derived from first-kind shifted polynomials that satisfy the homogeneous boundary conditions. The fractional derivatives are formulated to facilitate the solution process. The convergence analysis is studied for the suggested basis expansion; some numerical results are exhibited to verify the applicability and accuracy of the method.
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modified shifted Chebyshev polynomials, collocation method, Galerkin method, fractional BVPsHow to Cite
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Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2025 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.