Fractional boundary value problems: Analysis and numerical methods

By Neville J. Ford, Maria Luísa Morgado. 2011

90 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a26f6eb925adbfef108f52ccad2214c43c0784c5

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Citations in the corpus

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations (2014, background): “For some recent development on the topic, see [1], [2], [4], [5], [6], [7], [8], [9], [10], [11], [12], [14], [17], and the references therein.”
On the oscillation of fractional differential equations (2012, background): “A rigorous theory of FDE has been started quite recently, see for example - the books [4, 9, 11] and to mention only few papers related to ordinary FDE as [3, 6, 8].”
Nonpolynomial collocation approximation of solutions to fractional differential equations (2013, methodology): “The theory and numerical analysis of fractional differential equations has also been widely developed in the last decades, see for example [4], [6], [7], [8], [10], [12], [14], [16], [18] and the references therein.”
Fractional differential equations with dependence on the Caputo-Katugampola derivative (2016, methodology): “EN(t), such that lim N→∞ EN(t) = 0, ∀t ∈ [a,b]. Due to the complexity of solving analytically fractional diﬀerential equations, numerical tools are often applied to solve the given problems (see e.g. [3, 4, 7, 18, 20, 21]). We now present a simple but eﬃcient method to solve a fractional diﬀerential”
A discrete method to solve fractional optimal control problems (2014, background): “Such fractional problems are difficult to solve and numerical methods are often applied, which have proven to be efficient and reliable [1, 4, 5, 8, 13].”
A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations (2013, methodology): “Numerical schemes based on a shooting algorithm are discussed in [18].”
Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions (2012, background): “In addition to BVPs for ordinary differential equations, fractional differential inclusions [6, 7, 8], fractional integro-differential equations [2], fractional partial differential equations [3], and the numerical solution of such problems [12] are gaining increasing attention in the literature.”
The mean value theorems and a Nagumo-type uniqueness theorem for Caputo’s fractional calculus (2012, background): “for some α ∈ (0, 1), is combined with a condition of the form y(b) = y0 for some b > 0, have drawn a lot of attention [4, 7, 8].”
A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions (2013, background): “For some recent work on the topic, see ([7–23]) and the references therein.”