Numerical Simulations of Fractional Systems: An Overview of Existing Methods and Improvements

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Al-Alaoui operator and the new transformation polynomials for discretization of analogue systems (2008, unknown): “Al-Alaoui operator is a credible alternative to other discretization methods with wide range of applications in integer and fractional order discretization and other applications that require accurate and real time differentiation or integration [15–44].”
An improved non-classical method for the solution of fractional differential equations (2010, methodology): “Moreover, the design of fractional circuits and systems, including fractional control, have received strong attention [ 3 ,11,12,19,31].”
An optimal instrumental variable method for continuous-time fractional model identification (2008, background): “Refer to Aoun et al. (2004), for an extended discussion on this topic.”
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].”
Stability of Fractional-Order Systems with Rational Orders (2008, unknown): “It has been shown that commensurate system (14) is stable if the following condition is satisfied (also if the triplet A, B, C is minimal) [4, 35,59–61]: |arg(eig(A))| > q 2 , (29)”