Nelson Vieira

You are already at the latest version We investigate a time-fractional telegraph equation with variable coefficients involving Hilfer fractional derivatives. The problem is formulated as a Cauchy problem with Hilfer-type initial conditions. By applying the Fourier transform with respect to the spatial variable, we reduce the equation to a Hilfer-type fractional differential equation with variable coefficients.

1 INTRODUCTION The study of eigensolutions of the Laplace operator has been playing a major role in mathematical physics since the 19th century (see the book of Sommerfeld [1]).