Fourier transform analysis of random elliptic,parabolic and hyperbolic partial differential equations

In this study, information about the classification of Partial Differential Equations was given. Ordinary differential equations with random variable coefficients were solved with the help of Fourier Transform. In the field of basic engineering, it was desired to find solutions by using different models or methods. Fourier transform is an integral transform used in many fields such as mathematics, physics, heat flow, solution of partial differential equations, determination of frequency spectrum. The solutions of Hyperbolic, Parabolic, Elliptic Partial Differential equations with one- and two-dimensional random variable coefficients were examined with the help of Fourier Transform and their expected values and variances were found in the probability characteristics accordingly. In order to graph the values found, the graphical behavior of the found values was examined by using the Maple or Matlab program. In addition, definitions of the definition and properties of the Fourier Transform, literature review, and some probability distributions have been made.