A simple fractional-calculus approach to the solutions of the Bessel differential equation of general order and some of its applications
In many recent works, several authors demonstrated the usefulness of fractional calculus operators in the derivation of (explicit) particular solutions of a significantly large number of linear ordinary and partial differential equations of the second and higher orders. The main object of the present paper is to show how this simple fractional-calculus approach to the solutions of the classical Bessel differential equation of general order would lead naturally to several interesting consequences which include (for example) an alternative investigation of the power-series solutions obtainable usually by the Frobenius method. The methodology presented here is based largely upon some of the general theorems on (explicit) particular solutions of a certain family of linear ordinary fractional differintegral equations. (c) 2005 Elsevier Ltd. All rights reserved.
bessel differential equation fractional calculus power-series solutions frobenius method differintegral equations fuchsian (and non-fuchsian) equations linear (ordinary and partial) differential equations index law linearity property generalized leibniz rule bessel functions trigonometric functions