Local Hölder continuity for fractional nonlocal equations with general growth

Hölder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton-Jacobi Equations with Superquadratic Growth in the Gradient

Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi equations with a super-quadratic growth in the gradient variable are proved to be Hölder continuous, with a modulus depending only on the growth of the Hamiltonian. The proof involves some representation formula for nonlocal Hamilton-Jacobi equations in terms of controlled jump processes and a weak reverse inequality.

Fuzzy Local Fractional Differential Equations

Exact Solution for Nonlinear Local Fractional Partial Differential Equations

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

Singular limits for reaction-diffusion equations with fractional Laplacian and local or nonlocal nonlinearity

We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP equation. This rescaling is based on the exponential speed of propagation of the population. In particular we show that the only role of the fractional Laplac...

Mild Solutions for Fractional Differential Equations with Nonlocal Conditions

This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions d q xt/dt q −Axt ft, xt, Gxt, t ∈ 0, T, and x0 gx x 0 , in a Banach space X, where 0 < q < 1. General existence and uniqueness theorem, which extends many previous results, are given.