11 - Fractional differential equations with singular coefficients

Abstract

In this chapter using the Meijer transform method we solve equations with left-sided fractional Bessel derivatives on semiaxes of Gerasimov–Caputo type with constant coefficient. Also, we apply the one-dimensional direct and inverse Mellin integral transforms to derive particular solutions to ordinary linear nonhomogeneous differential equations with fractional Bessel operators. Finally, we generalize and apply Riesz B-potentials to solve some linear equations with Bessel operators acting by all variables.