Fractional-order logistic differential equation with Mittag–Leffler-type Kernel

In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations of each solution in terms of a formal power series. Some numerical approximations are implemented by using truncated series.Agencia Estatal de Investigación | Ref. PID2020-113275GB-I00Xunta de Galicia | Ref. ED431C 2019/0

On the fractional Allee logistic equation in the Caputo sense

In the framework of population models, logistic growth and fractional logistic growth has been analyzed. In some situations the so-called Allee effect gives more accurate approximation. In this work, fractional Allee differential equation in the Caputo sense is considered. The solution is obtained by considering formal power series. Numerical computations are presented to compare the truncating series with the classical Allee differential equation.Agencia Estatal de Investigación | Ref. PID2020-113275GB-I00Xunta de Galicia | Ref. Ref. ED431C 2019/0

Geología y Volcanología de islas volcánicas oceánicas: Canarias-Hawaii

Lecciones didácticas de volcanología de Canarias y Hawaii con abundancia de ilustracionesCaja General de Ahorros de Canaria

On fractional derivatives and primitives of periodic functions

We prove that the fractional derivative or the fractional primitive of a -periodic function cannot be a -periodic function, for any period , with the exception of the zero functionThe work of I. Area has been partially supported by the Ministerio de Economía y Competitividad of Spain under Grant MTM2012-38794-C02-01, cofinanced by the European Community fund FEDER. J. J. Nieto also acknowledges partial financial support by the Ministerio de Economía y Competitividad of Spain under Grant MTM2010-15314, cofinanced by the European Community fund FEDER.S

The number of reduced alignments between two DNA sequences

Background In this study we consider DNA sequences as mathematical strings. Total and reduced alignments between two DNA sequences have been considered in the literature to measure their similarity. Results for explicit representations of some alignments have been already obtained. Results We present exact, explicit and computable formulas for the number of different possible alignments between two DNA sequences and a new formula for a class of reduced alignments. Conclusions A unified approach for a wide class of alignments between two DNA sequences has been provided. The formula is computable and, if complemented by software development, will provide a deeper insight into the theory of sequence alignment and give rise to new comparison methods. AMS Subject Classification Primary 92B05, 33C20, secondary 39A14, 65Q30The authors are grateful to Prof. Marko Petkovs̆ek for helpful comments. The work of I. Area has been partially supported by the Ministerio de Economía y Competitividad of Spain under grant MTM2012–38794–C02–01, co-financed by the European Community fund FEDER. J.J. Nieto also acknowledges partial financial support by the Ministerio de Economía y Competitividad of Spain under grant MTM2010–15314, co-financed by the European Community fund FEDERS