Author(s): Ferreira, M. ; Rodrigues, M.M. ; Vieira, N.
Date: 2026
Persistent ID: http://hdl.handle.net/10400.8/14530
Origin: IC-online
Subject(s): Dirac factorization method; Time-fractional telegraph equation; Time-fractional diffusion equation; Fractional calculus; Hilfer derivatives; Mittag-Leffler functions; Fox H-functions
This paper examines a coupled system of two-term time-fractional diffusion Dirac-type equations. The system is derived by factorizing the multi-dimensional time-fractional telegraph equation with Hilfer fractional derivatives, using the Dirac method and a triplet of Pauli matrices. Solutions are obtained using operational methods provided by the combination of the Fourier transform in the space variable and the Laplace transform in the time variable. Key results include the discovery of novel Fourier transform pairs. These pairs relate specific Fourier kernels of bivariate Mittag-Leffler functions to Fox H-functions of two variables. This allows to obtain explicit solutions of the system in both Fourier-time and space-time domains. The asymptotic behaviour of these solutions is rigorously analysed, and graphical representations are generated. Further, we show that the factorization allows for the use of alternative triplets of Pauli matrices yielding related solutions. The results obtained can be generalised to the case of -Hilfer derivatives.
