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Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

Luchko, Yury, Trujillo, Juan (2007)

Fractional Calculus and Applied Analysis

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones. Whereas the Riemann-Liouville definition of a fractional derivative is usually employed in mathematical texts and not so frequently in applications, and the Grünwald-Letnikov definition – for numerical approximation of both Caputo and Riemann-Liouville fractional derivatives,...

Characterization of surjective convolution operators on Sato's hyperfunctions

Michael Langenbruch (2010)

Banach Center Publications

Let μ ( d ) ' be an analytic functional and let T μ be the corresponding convolution operator on Sato’s space ( d ) of hyperfunctions. We show that T μ is surjective iff T μ admits an elementary solution in ( d ) iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are 0 μ ( d ) ' such that T μ is not surjective on ( d ) .

Commutants of the Dunkl Operators in C(R)

Dimovski, Ivan, Hristov, Valentin, Sifi, Mohamed (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 44A35; 42A75; 47A16, 47L10, 47L80The Dunkl operators.* Supported by the Tunisian Research Foundation under 04/UR/15-02.

Commutative neutrix convolution products of functions

Brian Fisher, Adem Kiliçman (1994)

Commentationes Mathematicae Universitatis Carolinae

The commutative neutrix convolution product of the functions x r e - λ x and x s e + μ x is evaluated for r , s = 0 , 1 , 2 , ... and all λ , μ . Further commutative neutrix convolution products are then deduced.

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