arXiv subjects

Allan Peterson

Publications and source records attributed to Allan Peterson.

3 recordsLinked to original sources

arXiv2020

Lyapunov functions for fractional order h-difference systems

This paper presents some new propositions related to the fractional order $h$-difference operators, for the case of general quadratic forms and for the polynomial type, which allow proving the stability of fractional order $h$-difference systems, by means of the discrete fractional Lyapunov direct method, using general quadratic Lyapunov functions, and polynomial Lyapunov functions of any positive integer order, respectively. Some examples are given to illustrate these results.

math.CA↗

arXiv2018

Sturm Liouville Equations in the frame of fractional operators with Mittag-Leffler kernels and their discrete versions

Very recently, some authors have studied new types of fractional derivatives whose kernels are nonsingular. In this article, we study Sturm-Liouville Equations ($SLEs$) in the frame of fractional operators with Mittag-Leffler kernels. We formulate some Fractional Sturm-Liouville Problems ($FSLPs$) with the diffferential part containing the left and right sided derivatives. We investigate the self-adjointness, eigenvalue and eigenfunction properties of the corresponding Fractional Sturm-Liouville Operators ($FSLOs$) by using fractional integration by parts formulas. The nabla discrete version of our results are also established.

math.CA↗

arXiv2018

Existence and Uniqueness of Solutions of Nabla Fractional Difference Equations Tending to a Nonnegative Constant

In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem to be incomplete. By using Contraction Mapping Theorem, we establish conditions under which solutions exist and are unique and have certain asymptotic properties.

math.CA↗