Fractional calculus: models and numerical methods. - Baleanu, Dumitru; Baleanu, Dumitru; Diethelm, Kai; Scalas, Enrico; Trujillo, Juan J (Series on complexity, nonlinearity and chaos, 2012)
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 order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.