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α-Mellin Transform and One of Its Applications

Nikolova, Yanka — 2012

Mathematica Balkanica New Series

MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45 We consider a generalization of the classical Mellin transformation, called α-Mellin transformation, with an arbitrary (fractional) parameter α > 0. Here we continue the presentation from the paper [5], where we have introduced the definition of the α-Mellin transform and some of its basic properties. Some examples of special cases are provided. Its operational properties as Theorem 1, Theorem 2 (Convolution theorem) and Theorem 3 (α-Mellin...

Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Nikolova, Yanka;  Boyadjiev, Lyubomir — 2010

Fractional Calculus and Applied Analysis

Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12. The method of integral transforms based on using a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problem for the time-space fractional diffusion equation expressed in terms of the Caputo time-fractional derivative and a generalized Riemann-Liouville space-fractional derivative.

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