The numerical solution of linear multi-term fractional differential equations: systems of equations

By J. Edwards, Neville J. Ford, A. Simpson. 2002

183 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f430328f93c268eb35a9f45060dd9519933738b7

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In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations (2011, background): “[26] and Ford and Connolly [27], where they transferred the problem to a system of fractional differential equations, each of order at most unity.”
Numerical solution of multi‐term fractional differential equations (2009, unknown): “A numerical scheme for multi-term FDEs has been proposed in [9], which reduces the multi-term equation to a system of mixed fractional and ordinary differential equations of order ≤ 1.”
Solving a system of nonlinear fractional differential equations using Adomian decomposition (2006, background): “In contrast for solving the nonlinear FDE, one has to depend upon numerical solutions solely [8,9].”
Volterra integral equations and fractional calculus: Do neighboring solutions intersect? (2012, unknown): “, [6,8,9].”
A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations (2013, result): “We refer also to the recent papers [20–23] where fractional linear multi-step methods and predictor–corrector methods of Adams type for solving Cauchy problems of fractional differential equations are discussed.”
Spline collocation methods for seismic analysis of multiple degree of freedom systems with visco-elastic dampers using fractional models (2020, background): “It generalizes the notions of integer-order differentiation and n-fold integration (Atangana and Baleanu, 2016; Baleanu et al., 2011, 2012; Diethelm, 2010; Edwards et al., 2002; Gemant, 1936; Gorenflo and Mainardi, 1997; Kilbas et al., 2006; Magin, 2006; Podlubny, 1999; Sabatier et al., 2007; Tenrei”
Adomian decomposition: a tool for solving a system of fractional differential equations (2005, methodology): “We discuss convergence problem and present illustrations encompassing Bagley and Torvik [14] and fractional oscillation equations [8].”
OSCILLATORY BEHAVIOR OF A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH DAMPING (2013, methodology): “Many papers have investigated some aspects of fractional differential equations, such as the existence and uniqueness of solutions to Cauchy type problems, the methods for explicit and numerical solutions, and the stability of solutions, and we refer to [12–19].”