Differential equations with fractional boundary conditions and their applications

In this thesis, differential equations with boundary conditions involving fractional derivatives are discussed, especially on beam problems. Multiple-Time Scales method (Perturbation method) is used as the solution methodology. Mathematical model solutions are obtained and stability analysis is performed. The thesis consists of five sections. The first section is devoted to the introduction. In the second section, the basic definitions used in the thesis are introduced. In the third section, details and applications of the Perturbation method (Multiple-Time Scales method) are given. In the fourth section, forced vibration analysis of the Euler-Bernoulli beam is discussed as an application to differential equations with fractional boundary conditions. Assuming that the beam is under the harmonic external force, it is mentioned that the mathematical model of the beam is obtained by using Cauchy stress theory and approximate solutions are determined. Then, steady state solutions and their stability are examined. The last section includes the conclusion.