The main objective of this study remains in differential equations and their applications in problems related to vibrations in the part of civil engineering, more specifically, the mathematical modeling and methodology of integral transforms of Laplace and Fourier, addressing their definitions, properties, and applications of convolution theorems. In addition, we intend to study integrals and derivatives of order not whole, the so-called fractional calculus, its origin, main definitions and properties, aiming to work his modeling with differential equations of non-integer order, in order to refine the description given by its equation of entire order. With regard to applications, solving ordinary differential equations arising in engineering problems, we intend to propose and study the fractional version of differential equations related to problems arising from vibrations in the part of civil engineering, specifically related to the differential equations the problems of the simple harmonic oscillator and damped harmonic oscillator solutions and compare their solutions with their entire order. Finally, it is emphasized that all reports will be made in LaTeX, which will be valuable for future scientific work of the student, who has pretensions to follow the academic career.
News published in Agência FAPESP Newsletter about the scholarship: