Fractional Quasi-Bessel Equations

In this paper we consider fractional quasi-Bessel equations $$\sum _{i=1}^m{d}_i{x}^{{\alpha }_i+p_i}{D}^{{\alpha }_i}u(x)+(x^{\beta }-{\nu }^2)u(x)=0$$ and construct their existence and uniqueness theory in the class of fractional series. Our methodology allows us to obtain new results for a broad class of fractional differential equations including Cauchy-Euler and constant-coefficient equations.