On the behaviour of solutions of the fractional order differential equations

After the first section which presented historical development of the fractional calculus, in the second section general information has been presented to underlie of the next section.In the third section, firstly fractional differential equations and their solutions has been explained in light of the ordinary differential equations and Laplace transform which is one of the most useful method has been presented for the solutions. Lastly theorems that enable to find explicit solutions of the arbitrary order homogenous linear fractional differential equations with constant coefficient have been presented.In the fourth section has been mentioned about Bagley-Torvik equations which have an important role in applications and have oscillation solutions, and also mentioned about fractional differential equations that have damped oscillation solutions.In the fifth section which is the original part of this thesis have been presented some results about the more general form of the Bagley-Torvik equations that have oscillate solutions