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 …

In this paper, we are concerned with finding numerical solutions to the class of time–space
fractional partial differential equations: D tpu (t, x)+ κ D xpu (t, x)+ τ u (t, x)= g (t, x), 1< p< 2,(t …

In this paper, a novel compact operator is derived for the approximation of the Riesz
derivative with order α∈(1,2. The compact operator is proved with fourth-order accuracy …

This paper is concerned with numerical solutions of time-fractional nonlinear parabolic
problems by a class of $ L1 $-Galerkin finite element methods. The analysis of $ L1 …

In this paper, a linearized L1-Galerkin finite element method is proposed to solve the
multidimensional nonlinear time-fractional Schrödinger equation. In terms of a temporal …

The numerical solution of the time-fractional Black-Scholes model for European and
American options is presented using a local meshless collocation approach based on hybrid …

Current discretizations of variable-order fractional (V-OF) differential equations lead to
numerical solutions of low order of accuracy. This paper explores a high order numerical …

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 …

In this paper, an energy conservative Crank–Nicolson difference scheme for nonlinear Riesz
space-fractional Schrödinger equations is studied. We give a rigorous analysis of the …

A shifted Legendre collocation method in two consecutive steps is developed and analyzed
to numerically solve one-and two-dimensional time fractional Schrödinger equations …