Quasi-Bessel equations: existence and hyper-dimensionality

We introduce fractional quasi-Bessel equations
$$ \sum_{i=1}^{m}{d_ix^{\xi_i}}D^{\alpha_i}u\left(x\right)+\left(x^\beta-\nu^2\right)u\left(x\right)=0 $$
and construct their existence theory in the class of fractional series solutions. In order to find the parameters of the series, we derive the characteristic equation, which is surprisingly independent of the terms with non-matching parameters $\xi_i\neq\alpha_i$. As a direct corollary, the method allows to analyze quasi-Euler and constant-coefficient equations and is applicable to the existence result for elliptic-like PDEs with fractional Cauchy-Euler operator. We also arrive at a hyper-dimensionality phenomenon for certain fractional differential equations possessing "too many" linearly independent solutions. The theoretical findings are justified computationally.
The results are obtained jointly with L. Boyadjiev and J. Slepoi.
References: Fract. Calc. Appl. Anal. 2021, 2022; J. Math. Sci. 2022.