Unified construction of fractional generalized orthogonal bases

Abstract : A unified approach is presented for the synthesis of continuous-time fractional Generalized orthogonal bases including Laguerre-like, Kautz-like and the Generalized-Orthogonal-Basis-like(GOB-like) bases. They extend the definitions of their rational counterpart to fractional differentiation orders. Modes can either be chosen to be real or by pairs complex conjugate. Completeness of fractional Laguerre-like basis is demonstrated.
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https://hal.archives-ouvertes.fr/hal-00401591
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Rachid Malti, Mohamed Aoun, François Levron, Alain Oustaloup. Unified construction of fractional generalized orthogonal bases. Fractional Differentiation and its Applications., U-Books, pp.87-102, 2005, ISBN 3-86608-026-3. ⟨hal-00401591⟩

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