PROCESSED INTEGRALS

Author: RODRIGUEZ GERMA LUIS FRANCISCO.
Year: 2006.
University: LA LAGUNA [www.ull.es].
Place of defense: D.A.MATEMATICO.
Place of preparation: FACULTAD DE MATEMATICAS.

Summary: The framework within which it takes place is the thesis Calculation Fraccionario, which studies the so-called operators integracisn and derivacisn of fractional order. The mathematical models based on Differential Equations Fraccionarias, have proved to be a good tool to explain the dynamics ansmala many processes related to complex systems, in the most diverse areas of science and Ingenierma. This memory provides tools and mitodos to get solutions to some of these models Fractional. In Capmtulo 1, we introduce and study two new comprehensive processed, we call divisional, which is a particular case of H-transformacisn, whose nzcleo known funcisn H Fox. First, we studied the transformed integral call transform Mittag-Leffler which has the funcisn of Mittag-Leffler as nzcleo, which is a funcisn which plays an important role in the solucisn many fractional differential equations. The second transformed comprehensive studying, we call Transformed type Bessel, widely known transformed integral Kratzel, which is solucisn some ecuacisn differential divisional. It conducts an intensive study of such funcisn, including its estimacisn asintstica. In Capmtulo 2 of the report tabled an teorma allowing generalize classic nzmeros Stirling of the first kind s (n, k), with nyk natural, extending both parameters field complex. To that end we introduce the definicisn these generalized functions Stirling based on the use of fractional operators and found that the properties have been kept most important of nzmeros Stirling classic. This extensisn lays the groundwork for the possible introduction of new mitodos of aproximacisn numirica those arising from Riemann-Liouville and divisional Liouville. The Capmtulo 3 is dedicated to the fractional differential equations involving derivatives of Caputo and Riemann-Liouville. First divisional studying linear equations with constant coefficients, both in the case homogineo as in the non homogineo and dervadas of Caputo not in any sequential order positive. In continuacisn explores linear differential equations involving the derivative of Caputo sequentially. For this type of equations yields a theory generally analogous to the case of regular and discusses solutions explmcitas both in the case of equations with constant coefficients as in the ratios of variables. By zltimo in Capmtulo 4 the main goal is to demonstrate the potential to simulate through fractional differential equations, the dynamics of processes abnormal whose representacisn analmtica come given by functions contmnuas but not heavily differentials, such as the type functions Weierstrass . This opens the possibility of finding some models fensmenos that it is impossible simularlos through differential traditional models. This we see as some functions of this type are derived fractional at all points of an interval actual therefore these functions are solutions of differential equations divisional