Browsing Mathematics by Authors
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Algorithms for the fractional calculus: A selection of numerical methodsDiethelm, Kai; Ford, Neville J.; Freed, Alan D.; Luchko, Yury (Elsevier Science, 20050225)This article discusses how numerical algorithms can help engineers work with fractional models in an efficient way.

Analysis of fractional differential equationsDiethelm, Kai; Ford, Neville J. (Elsevier Science, 20020115)

Detailed error analysis for a fractional Adams methodDiethelm, Kai; Ford, Neville J.; Freed, Alan D. (Springer, 200405)This preprint discusses a method for a numerical solution of a nonlinear fractional differential equation, which can be seen as a generalisation of the Adams–Bashforth–Moulton scheme.

Multiorder fractional differential equations and their numerical solutionDiethelm, Kai; Ford, Neville J.; Technische Universität Braunschweig ; University College Chester (Elsevier, 20040715)This article considers the numerical solution of (possibly nonlinear) fractional differential equations of the form y(α)(t)=f(t,y(t),y(β1)(t),y(β2)(t),…,y(βn)(t)) with α>βn>βn−1>>β1 and α−βn1, βj−βj−11, 0

A Note on the WellPosedness of Terminal Value Problems for Fractional Differential Equations.Diethelm, Kai; Ford, Neville J.; GNS & TUBS, Braunschweig, Germany; Univerity of Chester (Journal of Integral Equations and Applications, Rocky Mountains Mathematics Consortium, 20181108)This note is intended to clarify some im portant points about the wellposedness of terminal value problems for fractional di erential equations. It follows the recent publication of a paper by Cong and Tuan in this jour nal in which a counterexample calls into question the earlier results in a paper by this note's authors. Here, we show in the light of these new insights that a wide class of terminal value problems of fractional differential equations is well posed and we identify those cases where the wellposedness question must be regarded as open.

Numerical analysis for distributed order differential equationsDiethelm, Kai; Ford, Neville J.; University of Chester (University of Chester, 200104)In this paper we present and analyse a numerical method for the solution of a distributed order differential equation.

Numerical solution methods for distributed order differential equationsDiethelm, Kai; Ford, Neville J. (Institute of Mathematics & Informatics, Bulgarian Academy of Sciences, 2005)This article discusses a basic framework for the numerical solution of distributed order differential equations.

Numerical solution of multiorder fractional differential equationsDiethelm, Kai; Ford, Neville J. (Elsevier, 2004)

Numerical solution of the Bagley Torvik equationDiethelm, Kai; Ford, Neville J. (Springer, 200209)

Pitfalls in fast numerical solvers for fractional differential equationsDiethelm, Kai; Ford, Judith M.; Ford, Neville J.; Weilbeer, Marc (Elsevier, 20060215)This preprint discusses the properties of high order methods for the solution of fractional differential equations. A number of fractional multistep methods are are discussed.

A predictor corrector approach for the numerical solution of fractional differential equationsDiethelm, Kai; Ford, Neville J.; Freed, Alan D. (Springer, 200207)This article discusses an Adamstype predictorcorrector method for the numerical solution of fractional differential equations.

Volterra integral equations and fractional calculus: Do neighbouring solutions intersect?Diethelm, Kai; Ford, Neville J.; Technische Universität Braunschweig ; University of Chester (Rocky Mountain Mathematics Consortium, 20120404)This journal article considers the question of whether or not the solutions to two Volterra integral equations which have the same kernel but different forcing terms may intersect at some future time.