The present state-of-the-art article is devoted to the analysis of new trends and recent results
carried out during the last 10 years in the field of fractional calculus application to dynamic …

A look into fractional calculus and their applications from the signal processing point of view
is done in this paper. A coherent approach to the fractional derivative is presented, leading …

This book provides efficient and reliable numerical methods for solving fractional calculus
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …

Classic Newtonian mechanics assumes that space and time are continuous everywhere.
The basic physical quantities (eg speed, acceleration and force) can be described by an …

“God made the integers; all else is the work of man” 1. For centuries, the ancients were
satisfied with using natural numbers called simply “numbers”. What we call irrational …

Fractional calculus has been used to model physical and engineering processes that are
found to be best described by fractional differential equations. For that reason we need a …

The study of fractional variational problems with derivatives in the sense of Caputo is a
recent subject in Newtonian fluids. In this article, the homotopy perturbation method (HPM) …

This paper is devoted to the numerical treatment of fractional differential equations. Based
on the Grünwald–Letnikov definition of fractional derivatives, finite difference schemes for …

In this article, a general formulation for the fractional-order Legendre functions (FLFs) is
constructed to obtain the solution of the fractional-order differential equations. Fractional …

We are concerned with linear and nonlinear multi-term fractional differential equations
(FDEs). The shifted Chebyshev operational matrix (COM) of fractional derivatives is derived …