Given the increasing number of proposals and definitions of operators in the scope of
fractional calculus, it is important to introduce a systematic classification. Nonetheless, many …

With the development of urban and rural infrastructure, the power system is enforced to
operate nearly at its full capacity which result in heavily stressed power grid operation …

In this paper we introduce a new fractional derivative with respect to another function the so-
called ψ-Hilfer fractional derivative. We discuss some properties and important results of the …

This paper discusses the concepts underlying the formulation of operators capable of being
interpreted as fractional derivatives or fractional integrals. Two criteria for required by a …

We introduce a truncated $ M $-fractional derivative type for $\alpha $-differentiable
functions that generalizes four other fractional derivatives types recently introduced by Khalil …

This book introduces a series of problems and methods insufficiently discussed in the field of
Fractional Calculus–a major, emerging tool relevant to all areas of scientific inquiry. The …

Artificial neural network (ANN) is the backbone of machine learning, specifically deep
learning. The interpolating and learning ability of an ANN makes it an ideal tool for …

In this paper, we present a Leibniz type rule for the ψ-Hilfer (ψ-H) fractional derivative
operator in two forms, one written in terms of the ψ-Riemann-Liouville (ψ-RL) fractional …

We propose a new fractional derivative, the Hilfer–Katugampola fractional derivative.
Motivated by the Hilfer derivative this formulation interpolates the well-known fractional …

The main subject of the monograph is the fractional calculus in the discrete version. The
volume is divided into three main parts. Part one contains a theoretical introduction to the …