Authors’ abstract: For a prescribed real number [1, 2), we give some sufficient conditions on the coefficients and such that every solution ]) of the linear differential equation
is bounded and fractal oscillatory near with the fractal dimension equal to . This means that oscillates near and the fractal (box-counting) dimension of the graph of is equal to as well as the dimensional upper Minkowski content (generalized length) of is finite and strictly positive. It verifies that admits similar kind of the fractal geometric asymptotic behaviour near like the chirp function , which often occurs in the time – frequency analysis and its various applications. Furthermore, this kind of oscillations is established for the Bessel, chirp and other types of damped linear differential equations given in the form
In order to prove the main results, we state a new criterion for fractal oscillations near of real continuous functions.