A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

Boost Software Business Products with Hybrid Development

This paper presents how new paradigms and methodologies for software development are changing rapidly in the last two years. In the current scenario where we live on, occurs a transition that, although slight, reflects the rapid manner in which the software production paradigms are reinvented due to the change of display devices and interaction with the end user. Studies indicate that in 2013 was the turn out of the internet access domain for mobile devices over the traditional desktop device, which is currently at around 60% mobile, against 40% desktop. This field will tend to grow in the coming years and it is expected that the use of internet for a desktop terminal tends to be less each day (comScore). In this context, the software industry has been re-invented and updated with respect to technologies that promote software and mobile applications, building products capable of responding to the user market. The development of software products, such as applications, must be put into production for different user environments, such as Web, iOS and Android in a way to enhance efficiency, optimization and productivity in the software development cycle (Langer, Arthur M.).