2022
DOI: 10.1155/2022/6261378
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Applying the Reproducing Kernel Method to Fractional Differential Equations with Periodic Conditions in Hilbert Space

Abstract: In this article, the reproducing kernel method is presented for the fractional differential equations with periodic conditions in the Hilbert space. This method gives an approximate solution to the problem. The approximate and exact solutions are displayed in the form of series in the reproduction kernel space. In addition, we provide an error analysis for this technique. The presented method is tested by some examples to show its precision.

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Cited by 2 publications
(3 citation statements)
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“…Finally, we consider the function space in Equation (11) on hB, and it is an RKHS with reproducing kernel in Equation (12).…”
Section: Function Spacementioning
confidence: 99%
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“…Finally, we consider the function space in Equation (11) on hB, and it is an RKHS with reproducing kernel in Equation (12).…”
Section: Function Spacementioning
confidence: 99%
“…Proof. The proof is straightforward by Theorem 1 when we constrained functions on H 2 (hB, d(ρ ⊗ µ)) with a reproducing kernel in Equation (12).…”
Section: Corollary 3 (Kepler Ball Case) For Any Functionmentioning
confidence: 99%
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