Modelling and Analysis of Fractional Order Systems using Ultradistributions
C.M.Grunfeld, M.C.Rocca
TL;DR
This paper introduces ultradistributions as a novel mathematical tool for solving fractional equations in fractional systems, unifying derivatives and integrals, with various applications demonstrated.
Contribution
It presents ultradistributions as a new approach to model and analyze fractional systems, combining derivatives and integrals into a single operation.
Findings
Ultradistributions effectively solve fractional equations.
Unified framework for derivatives and integrals in fractional calculus.
Applications demonstrate versatility of the method.
Abstract
In this paper we introduce a new mathematical tool to solve fractional equations representing models of fractional systems : The Ultradistributions. Ultradistributions permit us to unify the notion of integral and derivative in one only operation. Several examples of application of the results obtained are given.
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Taxonomy
TopicsAdvanced Control Systems Design · Numerical methods for differential equations