Abstract
In this paper, we use the fractional Legendre transform to treat the mixed boundary value problems on the unite sphere. We study the Laplace and Helmholtz operators on the unite sphere and coincide these operators with the fractional Sturm–Liouville problems. We apply the fractional Legendre transform to establish series approximations for the solutions of these problems. To obtain the unknown parts of solutions, we derive the Fredholm integral equations with the infinite series as separable kernels. We employ a technique for the integral equations to approximate the solutions in terms of the resolvent kernels.
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Communicated by Roberto Garrappa.
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Ansari, A. Comparative analysis for fractional Laplace and Helmholtz equations on sphere with mixed boundary conditions. Comp. Appl. Math. 42, 369 (2023). https://doi.org/10.1007/s40314-023-02533-1
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DOI: https://doi.org/10.1007/s40314-023-02533-1