Intra-hour photovoltaic power forecasting provides essential information for real time optimal
control of microgrids. At this purpose, a critical issue is the selection of the forecasting …

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 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 …

The fractal dimension is an indispensable tool bridging the two distinct fields of mathematics
namely, the fractional calculus and the fractal geometry. Many works have elucidated a …

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 …

In the present paper we construct second order shifted approximations for the first derivative
which have exponential and logarithmic generating functions. Applications of the …

The solutions of fractional differential equations (FDEs) have a natural singularity at the
initial point. The accuracy of their numerical solutions is lower than the accuracy of the …

In the present paper we use the expansion formula of the polylogarithm function to construct
approximations of the Caputo derivative which are related to the midpoint approximation of …

Fractional derivatives have found application in modeling various processes in different
fields of science. Finite difference schemes are a main approach for numerical solution of …

The aim of the report is to propose a method for construction of approximations of the
Caputo derivative whose weights have properties similar to the properties of the weights of …