In this work we discuss the solvability of Bessel's differential equation of order p, which is a particular case of the confluent hypergeometric equation, from the perspective of the theory of calculus of arbitrary order, also usually known as fractional calculus. In particular, in order to compare our method with the formulations in the literature, we raise some questions about interpretations of the Riemann-Liouville operators when acting on certain types of functions. In order to do so, we present the main fractional operators (Riemann-Liouville) as well as the fractional integrodifferential operator, which is a unified view of both integration and differentiation under a single operator.
Keywords:
fractional calculus; fractional differential equations; Bessel equation