1. The Mittag–Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation
- Author
-
Gustavo Abel Dorrego
- Subjects
INTEGRALS TRANSFORMS ,Matemáticas ,FRACTIONAL DIFFERENTIAL EQUATION ,01 natural sciences ,Matemática Pura ,symbols.namesake ,Mittag-Leffler function ,Generalizations of the derivative ,0101 mathematics ,CAPUTO FRACTIONAL DERIVATIVE ,Computer Science::Distributed, Parallel, and Cluster Computing ,Mathematics ,Applied Mathematics ,Operator (physics) ,010102 general mathematics ,Mathematical analysis ,Wave equation ,ULTRA-HYPERBOLIC OPERATOR ,Fractional calculus ,010101 applied mathematics ,Fourier transform ,Quadratic form ,HILFER FRACTIONAL DERIVATIVE ,symbols ,MITTAG–LEFFLER-TYPE FUNCTION ,RIEMANNundefinedLIOUVILLE FRACTIONAL DERIVATIVE ,Laplace operator ,Analysis ,FOX'S H-FUNCTION ,CIENCIAS NATURALES Y EXACTAS - Abstract
In this paper we study an n-dimensional generalization of time-fractional diffusion-wave equation, where the Laplacian operator is replaced by the ultra-hyperbolic operator and the time-fractional derivative is taken in the Hilfer sense. The analytical solution is obtained in terms of the Fox's H-function, for which the inverse Fourier transform of a Mittag–Leffler-type function that contains in its argument a positive-definite quadratic form is calculated. Fil: Dorrego, Gustavo. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
- Published
- 2016