The local fractional Burgers' equation (LFBE) is investigated from the point of view of local
fractional conservation laws envisaging a nonlinear local fractional transport equation with a …

A degenerate nonlinear nonlocal evolution equation is considered; it can be understood as
a porous medium equation whose pressure law is nonlinear and nonlocal. We show the …

arXiv:0812.4979v1 [math.AP] 29 Dec 2008 Page 1 arXiv:0812.4979v1 [math.AP] 29 Dec 2008
NONLINEAR DIFFUSION OF DISLOCATION DENSITY AND SELF-SIMILAR SOLUTIONS …

Analysis of local fractional coupled Helmholtz and coupled Burgers’ equations in fractal media
Page 1 AIMS Mathematics, 7(5): 8080–8111. DOI: 10.3934/math.2022450 Received: 02 …

This article utilizes the Aboodh residual power series and Aboodh transform iteration
methods to address fractional nonlinear systems. Based on these techniques, a system is …

We study a generalization of the porous medium equation involving nonlocal terms. More
precisely, explicit self-similar solutions with compact support generalizing the Barenblatt …

In this study, we prove that modified diffusion equations, including the generalized Burgers'
equation with variable coefficients, can be derived from the Black-Scholes equation with a …

We develop a general framework for finding error estimates for convection-diffusion
equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations …

The notion of Kruzhkov entropy solution was extended by the first author in 2007 to
conservation laws with a fractional Laplacian diffusion term; this notion led to well …

The fractional Laplacian $(-\Delta)^{\alpha/2} $ is the prototypical non-local elliptic operator.
While analytical theory has been advanced and understood for some time, there remain …