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 …

This book provides efficient and reliable numerical methods for solving fractional calculus
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …

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 …

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 …

This paper investigates chaotic behavior and stability of fractional differential equations
within a new generalized Caputo derivative. A semi–analytical method is proposed based …

This work proposes a robust ADI scheme on graded mesh for solving three-dimensional
subdiffusion problems. The Caputo fractional derivative is discretized by L1 scheme, where …

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 …

This paper proposes a linearized fast high-order time-stepping scheme to solve the time–
space fractional Schrödinger equations. The time approximation is done by using the fast L2 …

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 …

For the first time in literature, semi-implicit spectral approximations for nonlinear Caputo time-
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …