Erratum to: “Fractional non-Archimedean calculus in one variable”

One-Variable and Multi-Mariable Calculus on a Non-Archimedean Field Extension of the Real Numbers∗

New elements of calculus on a complete real closed non-Archimedean field extension F of the real numbers R will be presented. It is known that the total disconnectedness of F in the topology induced by the order makes the usual (topological) notions of continuity and differentiability too weak to extend real calculus results to F . In this paper, we introduce new stronger concepts of continuity...

One Variable Advanced Calculus

One-dimensional Optimization on Non-archimedean Fields

One dimensional optimization on non-Archimedean fields is presented. We derive first and second order necessary and sufficient optimality conditions. For first order optimization, these conditions are similar to the corresponding real ones; but this is not the case for higher order optimization. This is due to the total disconnectedness of the given non-Archimedean field in the order topology, ...

Matrix approach to discrete fractional calculus III: non-equidistant grids, variable step length and distributed orders.

In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, ...

Non-archimedean Dynamics in Dimension One: Lecture Notes

These notes for my short course at the 2010 Arizona Winter School are a bit long, but for two (hopefully good) reasons. The first is that these notes will form the core of a book that I am planning to write on the topic, and therefore I often proved even relatively minor lemmas in far greater detail than is usually appropriate for a set of lecture notes. The second, and more relevant for studen...