TY - CHAP A1 - Carlos Alberto Torres Martínez A2 - Carlos Fuentes ED1 - Fernando Brambila Y1 - 2017-06-14 PY - 2017 T1 - Applications of Radial Basis Function Schemes to Fractional Partial Differential Equations N2 - Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis. BT - Fractal Analysis SP - Ch. 1 UR - https://doi.org/10.5772/67892 DO - 10.5772/67892 SN - 978-953-51-3192-2 PB - IntechOpen CY - Rijeka Y2 - 2021-07-25 ER -