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 …

Variable-order fractional operators were conceived and mathematically formalized only in
recent years. The possibility of formulating evolutionary governing equations has led to the …

Fractional order models involving nonlinearity are remarkable for having substantial
application in real-world. The present determination is due to obtain applicable wave …

We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form
of a series of Riemann–Liouville fractional integrals, which brings out more clearly the non …

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 …

Up to now we have introduced a fractional derivative definition for special simple function
classes. In the following section we will present common generalizations for arbitrary …

Modern economics was born in the Marginal revolution and the Keynesian revolution. These
revolutions led to the emergence of fundamental concepts and methods in economic theory …

Many possible definitions have been proposed for fractional derivatives and integrals,
starting from the classical Riemann–Liouville formula and its generalisations and modifying …

The paper discusses the characteristic properties of fractional derivatives of non-integer
order. It is known that derivatives of integer orders are determined by properties of …

In this article, we propose a new factorization technique for nonlinear ODEs involving local
fractional derivatives for the first time. By making use of the traveling-wave transformation …