Utilizzando una generalizzazione della disuguaglianza di Gronwall si fornisce una stima puntuale per la soluzione dell’equazione lineare integrale di Volterra di seconda specie. Tale stima può essere applicata utilmente anche nello studio della stabilità di equazioni di evoluzione per mezzi continui.
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major contributions during the period 1966-2010.
In this paper, we define a -integral, i.e. an integral defined by means of partitions of unity, on a suitable compact metric measure space, whose measure is compatible with its topology in the sense that every open set is -measurable. We prove that the -integral is equivalent to -integral. Moreover, we give an example of a noneuclidean compact metric space such that the above results are true.
This note contains a proof of the existence of a one-to-one function of onto itself with the following properties: is a rational-linear automorphism of , and the graph of is a non-measurable subset of the plane.
An exact Radon-Nikodym derivative is obtained for a pair (I,J) of positive linear functionals, with J absolutely continuous with respect to I, using a notion of exhaustion of I on elements of a function algebra lattice.