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Obtaining Voigt Functions Via Quadrature Formula for the Fractional in Time Diffusion and Wave Problem

In many given physical problems and in the course of dispersion curve through a spectral line under the inﬂuence of the Doppler-eﬀect and in collision damping, the Voigt functions have been widely utilized. By taking advantage of the fractional calculus in spectral theory and the Sturm-Liouville problems, in this paper, we obtain the Voigt functions via the quadrature formulae of one dimensional fractional in time evolution diﬀusion and wave problems consisting of diﬀerent initial and inhomogeneous boundary conditions.