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 …

We develop proper correction formulas at the starting k-1 steps to restore the desired k th-
order convergence rate of the k-step BDF convolution quadrature for discretizing evolution …

We introduce a modified L1 scheme for solving time fractional partial differential equations
and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and …

The aim of this paper is to develop and analyze high-order time stepping schemes for
approximately solving semilinear subdiffusion equations. We apply the convolution …

In this paper, a novel optimal fourth-order fractional-compact-type numerical differential
formula for the Riesz derivatives is derived by constructing the appropriate generating …

In this paper, a kind of the differential equation including a time-fractional sub-diffusion
equation is considered. Through this memorandum, a well-known technique, in the time …

In this paper, we consider an approximation of the Caputo fractional derivative and its
asymptotic expansion formula, whose generating function is the polylogarithm function. We …

In this paper we derive the fourth-order asymptotic expansions of the trapezoidal
approximation for the fractional integral and the $ L1 $ approximation for the Caputo …