On rules of derivation with complex order for analytic and branched functions

Campos, L.M.B.C.

Displaying similar documents to “On rules of derivation with complex order for analytic and branched functions”

On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira.

Campos, L.M.B.C. (1990)

International Journal of Mathematics and Mathematical Sciences

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Integral transforms with generalized Legendre functions as kernels

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Theory of non-analytic Functions of a complex Variable

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Analytic functions in general analysis

Angus E. Taylor (1937)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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New approach to the fractional derivatives.

Trenčevski, Kostadin (2003)

International Journal of Mathematics and Mathematical Sciences

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On the solution of some simple fractional differential equations.

Campos, L.M.B.C. (1990)

International Journal of Mathematics and Mathematical Sciences

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Elementary Solution of Vecua Equation With Analytic Coefficients on Z, $o v e r l i n e Z$

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On a new Subclass of Analytic P-valent Functions

Shigeyoshi Owa (1984)

Publications de l'Institut Mathématique

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Failure of analytic hypoellipticity in a class of differential operators

Ovidiu Costin, Rodica D. Costin (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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For the hypoelliptic differential operators $P = \partial_{x}^{2} + {(x^{k} \partial_{y} - x^{l} \partial_{t})}^{2}$ introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of $k$ and $l$ left open in the analysis, the operators $P$ also fail to be analytic hypoelliptic (except for $(k, l) = (0, 1)$ ), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of eigenvalues of a non-self-adjoint operator.

Numerical Results for the Generalized Mittag-Leffler Function

Seybold, H. J., Hilfer, R. (2005)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 33E12, 33FXX PACS (Physics Abstracts Classification Scheme): 02.30.Gp, 02.60.Gf Results of extensive calculations for the generalized Mittag-Leffler function E0.8,0.9(z) are presented in the region −8 ≤ Re z ≤ 5 and −10 ≤ Im z ≤ 10 of the complex plane. This function is related to the eigenfunction of a fractional derivative of order α = 0.8 and type β = 0.5.