Finite difference approximations for fractional advection-dispersion flow equations

TL;DR: In this article, the authors study the volatility surface of the Black-Scholes delta and derive numerical methods based on judicial finite-difference approximations for fractional derivatives.

TL;DR: This letter develops high order finite difference weighted essentially non-oscillatory (WENO) schemes for fractional differential equations that have high order accuracy in smooth regions and maintains a sharp discontinuity transition.

TL;DR: In this article, the Riesz space fractional derivative and the Riemann-Liouville type of the Laplacian operator are approximated using finite difference and finite element methods, respectively.

TL;DR: In this article, the numerical methods for solving fractional equations, which are divided into the fractional differential equations (FDEs), time fractional, space fractional and space-time-fractional partial differential equations, are discussed.

TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.

TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.

TL;DR: In this article, the authors consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einstein's relation in the presence of disorder, and illustrate the theoretical models by describing many physical situations where anomalous (non-Brownian) diffusion laws have been observed or could be observed.