Applications of fractional calculus in civil Engineering

Abstract

This study focuses on differential equations and their applications in civil engineering problems, more specifically, the mathematical modeling and methodology of the Laplace integral transform, covering its definition, properties, convolution theorem, and applications, as well as working with the problem of inversion this transformed. Furthermore, we intend to study integrals and derivatives of non-integer order, the so-called fractional calculus, its origin, main definitions, and properties, aiming his modeling work with differential equations of non-integer order in order to refine the description given by its equation entire order. With respect to applications, besides solving ordinary differential equations arising from engineering problems, aims to propose and evaluate the fractional release of differential equations related problems resulting from the vibrations in civil engineering, more particularly the differential equations relating the problems of the simple harmonic oscillator and the damped harmonic oscillator and compare their solutions with their entire order solutions. (AU)