This paper discusses the modeling via mathematical methods based on fractional calculus, using Caputo fractional derivative. From the fractional models associated with harmonic oscillator, logistic equation and Malthusian ...

In this paper we study an n-dimensional generalization of timefractional diffusion-wave equation, where the Laplacian operator is replaced by the ultra-hyperbolic operator and the time-fractional derivative is taken in the ...

This paper presents two models for hepatitis B, both given by fractional differential equations. The first model is formulated without parameters that indicate drug therapy, while the second one considers the drug therapy. ...

The paper introduces a new integral operator which generalizes the Prabhakar integral operator. The boundedness on the space of continuous functions and on the space of Lebesgue integrable functions on an interval is ...

This paper presents the design of a fractional controller, which is applied to a fractional MISO model for cement rotary kiln. The designed controller is a combination of a fractional PID and a Linear Quadratic Regulator ...

In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we ...

The aim of this paper is to introduce an alternative de nition for the k-Riemann-Liouville fractional derivative given in [6] and whose advantage is that it is the left inverse of the corresponding of k-Riemann-Liouville ...

Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the ...

A generalization of the fractional logistic equation by using k-Caputo derivative is introduced. Also a solution that can be expressed en terms of the k-Mittag-Le er function is obtained. The development of this paper ...