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Numerical methods for fractional partial differential equations
In this review paper, we are mainly concerned with the finite difference methods, the
Galerkin finite element methods, and the spectral methods for fractional partial differential …
Galerkin finite element methods, and the spectral methods for fractional partial differential …
[کتاب][B] Theory and numerical approximations of fractional integrals and derivatives
C Li, M Cai - 2019 - SIAM
Fractional calculus, which has two main features—singularity and nonlocality from its origin—
means integration and differentiation of any positive real order or even complex order. It has …
means integration and differentiation of any positive real order or even complex order. It has …
Numerical approaches to fractional integrals and derivatives: a review
Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two
main characteristics—singularity and nonlocality—has attracted increasing interest due to its …
main characteristics—singularity and nonlocality—has attracted increasing interest due to its …
Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations
This paper investigates chaotic behavior and stability of fractional differential equations
within a new generalized Caputo derivative. A semi–analytical method is proposed based …
within a new generalized Caputo derivative. A semi–analytical method is proposed based …
Analysis and approximation of a fractional Cahn--Hilliard equation
We derive a fractional Cahn--Hilliard equation (FCHE) by considering a gradient flow in the
negative order Sobolev space H^-α, α∈0,1, where the choice α=1 corresponds to the …
negative order Sobolev space H^-α, α∈0,1, where the choice α=1 corresponds to the …
Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative
Recently a new fractional differentiation was introduced to get rid of the singularity in the
Riemann-Liouville and Caputo fractional derivative. The new fractional derivative has then …
Riemann-Liouville and Caputo fractional derivative. The new fractional derivative has then …
A novel high order space-time spectral method for the time fractional Fokker--Planck equation
The fractional Fokker--Planck equation is an important physical model for simulating
anomalous diffusions with external forces. Because of the nonlocal property of the fractional …
anomalous diffusions with external forces. Because of the nonlocal property of the fractional …
[HTML][HTML] Numerical solution of the time fractional Black–Scholes model governing European options
When considering the price change of the underlying fractal transmission system, a
fractional Black–Scholes (BS) model with an α-order time fractional derivative is derived. In …
fractional Black–Scholes (BS) model with an α-order time fractional derivative is derived. In …
A two-grid mixed finite element method for a nonlinear fourth-order reaction–diffusion problem with time-fractional derivative
In this article, we develop a two-grid algorithm based on the mixed finite element (MFE)
method for a nonlinear fourth-order reaction–diffusion equation with the time-fractional …
method for a nonlinear fourth-order reaction–diffusion equation with the time-fractional …
A fourth-order approximation of fractional derivatives with its applications
A new fourth-order difference approximation is derived for the space fractional derivatives by
using the weighted average of the shifted Grünwald formulae combining the compact …
using the weighted average of the shifted Grünwald formulae combining the compact …