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 ...

Based on the k-Mittag-Lefler function and the k-α-Exponential Function we introduce families of functions that allows us define new fractional trigonometric functions that contain the classical trigonometric functions ...

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. ...

This work deals with mathematical modeling applied to the Human Immunodeficiency Virus. Mathematical aspects analysis is presented, discussed and reviewed. A new model based on the Fractional Calculus theory is proposed. ...

This paper presents the analysis of three classes of fractional differential equations appearing in the field of fractional adaptive systems, for the case when the fractional order is in the interval alpha is an element ...

The aim of this paper is to introduce an alternative definition 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-RiemannLiouville ...

The new result presented here is a theorem involving series in the three-parameter Mittag-Le er function. As a by-product, we recover some known results and discuss corollaries. As an application, we obtain the solution ...

In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called ...