The Bessel function J 0 in fractional differential equations

Spherical Bessel functions have many important applications in engineering, optic and science. In this work, wich is a continuation of the error function in fractional differential equations, it is shown how solve the fractional differential equation d α y d x α = j 0 ( x ) , y ( k ) ( 0 ) = 0 , k = 0 , … m − 1 ,   with m − 1 < α ≤ m , m ∈ Ν , where the nonhomogenous part is the function Bessel spherical J 0 ( x ).