Numerical solution of Caputo fractional differential equations with infinity memory effect at initial condition

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dc.creatorEduardo Mazoni Andrade Marçal Mendes
dc.creatorGustavo Henrique Oliveira Salgado
dc.creatorLuis Antonio Aguirre
dc.date.accessioned2025-04-25T14:54:43Z
dc.date.accessioned2025-09-09T00:11:17Z
dc.date.available2025-04-25T14:54:43Z
dc.date.issued2018
dc.identifier.doihttps://doi.org/10.1016/j.cnsns.2018.09.022
dc.identifier.issn1007-5704
dc.identifier.urihttps://hdl.handle.net/1843/81854
dc.languageeng
dc.publisherUniversidade Federal de Minas Gerais
dc.relation.ispartofCommunications in nonlinear science and numerical simulation
dc.rightsAcesso Restrito
dc.subjectSistemas dinâmicos
dc.subjectSistemas não lineares
dc.subject.otherA new method for computing numerical solutions of fractional differential equations in the sense of Riemann-Liouville definition, Use of Caputo definition in the case of non zero initial conditions, The infinite memory effect of fractional calculus is adequately dealt with
dc.subject.otherFractional-order systems, Simulation, Discretization
dc.subject.otherfractional calculus has been applied to various different problems in several fields of natural science, economics, physics and chemistry. In such studies, a common way of analysis is to propose a mathematical model written as a fractional-order differential equation for the system being investigated and to compare the numerical solutions of the model to data obtained from the system. A key point in such investigations is to verify if dynamical features that are present in the data are also found in the solutions obtained by numerical integration
dc.titleNumerical solution of Caputo fractional differential equations with infinity memory effect at initial condition
dc.typeArtigo de periódico
local.citation.epage247
local.citation.spage237
local.citation.volume69
local.description.resumoThe simulation of linear and nonlinear fractional-order systems on digital computers is investigated. The Grünwald-Letnikov definition of the fractional-order derivative is analyzed in the light of the initial conditions and as a consequence a new modified scheme for the discretization and simulation of fractional order systems is proposed. For this new scheme, it will be shown a new result where Riemann-Liouville derivative with the lower limit at infinity is related with a Caputo derivative with the lower limit at a finite real value allowing the infinite memory effect of fractional calculus to be adequately dealt with. To illustrate the use of the proposed method, the numerical solution of a linear fractional-order system is compared to the available analytical solution and, in the case of nonlinear fractional systems, the solution is compared to one provided by using the Adams method proposed by Diethelm
local.publisher.countryBrasil
local.publisher.departmentENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICA
local.publisher.initialsUFMG
local.url.externahttps://www.sciencedirect.com/science/article/pii/S1007570418303022

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