The successive iteration (started by Lagrange and Gauss) produces a new mean from two given ones. Several examples of matrix means are given that require the proof of the matrix monotonicity of the corresponding representing function. The paper contains extensions of the logarithmic mean and it is obtained that the Stolarsky mean can be used also for matrices. 2000 Mathematics Subject Classific...

In recent years, there has been a growing interest on non-localmodels because of their relevance in many practical applications. Awidely studied class non-local models involves fractional orderoperators. They usually describe anomalous diffusion. Inparticular, these equations provide more faithful representationof the long-memory and nonlocal dependence diffusion fractaland porous media, heat f...