Ferroelectrics are complex structured media that exhibit fractal properties and memory
effects in terms of a number of dynamic characteristics. The most relevant applications of …

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 …

It is well known that using high-order numerical algorithms to solve fractional differential
equations leads to almost the same computational cost with low-order ones but the accuracy …

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 …

In this paper, we use the asymptotic expansions of the binomial coefficients and the weights
of the L1 approximation to obtain approximations of order 2-α 2-α and second-order …

Approximating the Hadamard finite-part integral by the quadratic interpolation polynomials,
we obtain a scheme for approximating the Riemann-Liouville fractional derivative of order …

In this paper we construct approximations for the Caputo derivative of order 1-α, 2-α, 2 and 3-
α. The approximations have weights k− 1− α/Γ (-α) and 0.5 ((k+ 1)− α-(k-1)− α)/Γ (1-α), and …

In this paper we consider constructions of first derivative approximations using the
generating function. The weights of the approximations contain the powers of a parameter …

Abstract The Kolmogorov–Avrami theory of crystallization is widely used for simulation of
polarization switching kinetics in ferroelectrics. In the present study, a fractional modification …

Abstract By rewriting the Riemann–Liouville fractional derivative as Hadamard finite-part
integral and with the help of piecewise quadratic interpolation polynomial approximations, a …