This study focuses on differential equations and their applications in problems related to production engineering, more specifically, to study 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 of production engineering, specifically the logistic equation of Verhulst model and applied to studies on the production and import of natural gas in Brazil. Finally, it is emphasized thatall reports will be made in LaTeX, which will be of great value to future scientific work of the student.
News published in Agência FAPESP Newsletter about the scholarship: