| Abstract: |
| We discuss the methods for constructing solutions in the form of series. These techniques assist in assessing well-posedness and, in some cases, lead to representations involving classical special functions. We highlight multi-series approaches, particularly solutions expressed as double and triple series. We address the fundamental sets of solutions and introduce new existence, uniqueness, and non-uniqueness results for linear fractional differential equations, including constant-coefficient, Cauchy-Euler and quasi-Bessel equations
$$
\sum_{i=1}^{m}d_i x^{\alpha_i+p_i}D^{\alpha_i} u(x) + (x^\beta - \nu^2)u(x)=0.
$$
Analytic findings are supported by computations. |
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