Analysis of Solutions of Some Multi-Term Fractional Bessel Equations

We construct the existence theory for generalized fractional Bessel differential equations and find solutions in form of or logarithmic power series. figure out cases when series solution is unique, non-unique, does not exist. The uniqueness theorem space Cp proved corresponding initial value problem. are concerned with following homogeneous equation $$\sum\limits_{i = 1}^m {{d_i}{x^{{\alpha _i}}}} {D^{{\alpha _i}}}u\left( x \right) + \left( {{x^\beta } - {v^2}} \right)u\left( 0,\,{\alpha _i} >0,\,\beta >0,$$ which includes standard classical as particular cases. Mostly, we consider derivatives Caputo sense positive coefficients di. Our leads to a threshold admissible ?2, perfectly fits known results. findings supported by several numerical examples counterexamples that justify necessity imposed conditions. key point investigation forming proper leading an algebraic characteristic equation. Depending on its roots their multiplicity/complexity, system linearly independent solutions.