217 citations · 1.3k across the 28 of their papers we have counts for
31 papers
The fractional d'Alembert's formulas
Cheng-Gang Li, Miao Li, Sergey Piskarev +1
In this paper we develop generalized d'Alembert's formulas for abstract fractional integro-differential equations and fractional differential equations on Banach spaces. Some examp…
Space-Time Duality and High-Order Fractional Diffusion
James F. Kelly, Mark M. Meerschaert
Super-diffusion, characterized by a spreading rate of the probability density function , where is time, may be mode…
Semi-fractional diffusion equations
Peter Kern, Svenja Lage, Mark M. Meerschaert
It is well known that certain fractional diffusion equations can be solved by the densities of stable Lévy motions. In this paper we use the classical semigroup approach for Lévy p…
Petrov-Galerkin Method for Fully Distributed-Order Fractional Partial Differential Equations
Mehdi Samiee, Ehsan Kharazmi, Mohsen Zayernouri +1
Distributed-order PDEs are tractable mathematical models for complex multiscaling anomalous transport, where derivative orders are distributed over a range of values. We develop a…
What Is the Fractional Laplacian?
Anna Lischke, Guofei Pang, Mamikon Gulian +8
The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in math…
A Unified Spectral Method for FPDEs with Two-sided Derivatives; A Fast Solver
M. Samiee, M. Zayernouri. Mark M. Meerschaert
We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form $ _{0…