The Mittag–Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation. Issue 5 (3rd May 2016)

• Record Type: Journal Article
• Authors: Dorrego, Gustavo A.
• Is Part Of: Integral transforms and special functions. Volume 27:Issue 5(2016)
• Page Start: 392
• Page End: 404
• Publication Date: 2016-05-03
• Subjects: Fractional differential equation -- Hilfer fractional derivative -- Caputo fractional derivative -- Riemann–Liouville fractional derivative -- Mittag–Leffler-type function -- Fox's H-function -- integrals transforms -- ultra-hyperbolic operator; 26A33 -- 33E12 -- 33E20 -- 35R11; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2016.1144185
• Languages: English
• ISSNs: 1065-2469

Abstract

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.