In this review paper, we are mainly concerned with the numerical methods for solving
fractional equations, which are divided into the fractional differential equations (FDEs), time …

This paper proposes an optimization method for solving a general form of nonlinear
fractional optimal control problems (NFOCP) governed by nonlinear fractional dynamical …

Many PDEs involving fractional Laplacian are naturally set in unbounded domains with
underlying solutions decaying slowly and subject to certain power law. Their numerical …

A linearized spectral Galerkin/finite difference approach is developed for variable fractional-
order nonlinear diffusion–reaction equations with a fixed time delay. The temporal …

This paper presents a new approach for solving fractional delay differential equations of
variable order using the spectral element method. The proposed method overcomes the …

Time-dependent fractional partial differential equations typically require huge amounts of
memory and computational time, especially for long-time integration, which taxes …

In this paper, we propose an adaptive procedure, recently developed for fractional ordinary
differential equations, for the solutions of time-fractional advection–diffusion–reaction …

We introduce a new general class of nonlinear variable order fractional partial differential
equations (NVOFPDE). The NVOFPDE contains, as special cases, several partial differential …

Variable-exponent fractional models attract increasing attentions in various applications,
while the rigorous analysis is far from well developed. This work provides general tools to …

Excessive synchronizations of neurons in the brain networks can be a reason for some
episodic disorders such as epilepsy. In this paper, we simulate neural dynamic models and …