Analysis of Fractional Differential Equations

By Kai Diethelm, Neville J. Ford. 2002

3,846 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/cac7c06a93524b8abfec424508af694e95e0c843

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Citations in the corpus

Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations (2009, positive): “It is known (see for example the discussion in [7]) that the exact solution to a multi-term equation is stable with respect to small perturbations in the order(s).”
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density (2013, background): “to [11], [15], or [32].”
The Variable-Order Fractional Calculus of Variations (2018, background): “36 3 Expansion formulas for fractional derivatives (Džrbašjan and Nersesjan, 1968) and (Rabotnov, 1969), has found many applications and seems to be more suitable to model physical phenomena (Dalir and Bashour, 2010; Diethelm, 2004; Machado et al., 2010; Murio and Mej́ıa, 2008; Singh, Saxena and Kum”
Some properties of Prabhakar-type fractional calculus operators (2015, background): “alculus. For more in-depth information, applications and related topics it is possible to consult some of the classical references, e.g. Samko et al. [25], Podlubny [23], Kilbas et al. [18], Diethelm [8], Gorenﬂo et al. [15], Mainardi [20]. We also suggest the reader to consult the references listed”
Existence results for boundary value problems with non-linear fractional differential equations (2008, background): “[1,14,15], El-Sayed [16–18], Kaufmann and Mboumi [19], Kilbas and Marzan [20], Mainardi [5], Momani and Hadid [21], Momani et al.”
Positive solutions of fractional differential equations with derivative terms (2012, background): “Introduction Fractional calculus is a generalization of ordinary differentiation and integration to arbitrary non-integer order.”
On a discrete fractional three-point boundary value problem (2012, background): “For example, the papers [2,11,12,14,17,24,30] each attend to various theoretical properties of the continuous fractional calculus.”
Fractional high order methods for the nonlinear fractional ordinary differential equation (2007, background): “[4].”
Existence and Uniqueness results for a class of Generalized Fractional Differential Equations (2014, methodology): “The proof of this theorem uses the following lemma, which asserts the connection between a FDE and the corresponding Volterra type integral equation [7, 8].”