The subject of fractional calculus and its applications (that is, convolution-type pseudo-
differential operators including integrals and derivatives of any arbitrary real or complex …

In this study, a harmonic oscillator with position-dependent mass is investigated. Firstly, as
an introduction, we give a full description of the system by constructing its classical …

In this paper, we define left and right Caputo fractional sums and differences, study some of
their properties and then relate them to Riemann–Liouville ones studied before by Miller KS …

Generalization of fractional differential operators was subjected to an intense debate in the
last few years in order to contribute to a deep understanding of the behavior of complex …

In this work, the variational iteration method (VIM) is used to solve a class of fractional
optimal control problems (FOCPs). New Lagrange multipliers are determined and some new …

We introduce a discrete-time fractional calculus of variations on the time scale (hZ) a, a∈ R,
h> 0. First and second order necessary optimality conditions are established. Examples …

Covering fractional order theory, simulation and experiments, this book explains how
fractional order modelling and fractional order controller design compares favourably with …

This paper presents a numerical method for solving a class of fractional optimal control
problems (FOCPs). The fractional derivative in these problems is in the Caputo sense. The …

We investigate two types of dual identities for Caputo fractional differences. The first type
relates nabla and delta type fractional sums and differences. The second type represented …

Neurotechnology has made great strides in the last 20 years. However, we still have a long
way to go to commercialize many of these technologies as we lack a unified framework to …