Abstract We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian of the underlying control problems/games along dual distributions agents. methods monotone, stable, and consistent, we prove convergence subsequences (i) degenerate equations in one space dimension (ii) nondegenerate arbitrary dimensions. also give...

The purpose of this paper is to compare the solutions of one-dimensional boundary value problems corresponding to classical, fractional and nonlocal diffusion on bounded domains. The latter two diffusions are viable alternatives for anomalous diffusion, when Fick’s first law is an inaccurate model. In the case of nonlocal diffusion, a generalization of Fick’s first law in terms of a nonlocal fl...

The diffusion equations with the local and the nonlocal fractional derivatives have been used to describe the flow through disorder media. Recently, the variational iteration method is successfully developed to find approximate solutions of the two kinds of fractional differential equations. This study reveals the new development of the method and compares the applications in two types of fract...

The spectral bound, s(αA + βV), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in β ∈ R. Kato's result is shown here to imply, through an elementary "dual convexity" lemma, that s(αA + βV) is also convex in α > 0, and notably, ∂s(αA + βV)/∂α ≤ s(A). Diffusions typically have s(A) ≤ 0, so that for diffusions with spa...

In this paper, local and nonlocal image processing are unified, within the same framework, by defining discrete derivatives on weighted graphs. These discrete derivatives allow to transcribe continuous partial differential equations and energy functionals to partial difference equations and discrete functionals over weighted graphs. With this methodology, we consider two gradient-based problems...

French and Polish teams have a record of successful collaborations which resulted in methods and results that are actually attracting a growing interest of the applied mathematics community. In this new project, the participants aim at understanding the role of anomalous diffusions in two important classes of nonlinear evolution equations: kinetic equations with a Lévy-Fokker-Planck operator an...

Nonlinear diffusions have successfully been employed to perform a variety of tasks in image processing. In the context of denoising, the Perona-Malik equation is a particularly successful example. In spite of its cherished qualities, it is mathematically ill-posed and has some practical short-comings. In this short paper a new nonlocal nonlinear diffusion is reported upon, which is locally well...