FRACTIONAL CALCULUS AND WAVES IN LINEAR VISCOELASTICITY

By M. T. Cicero. 2012

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An historical perspective on fractional calculus in linear viscoelasticity (2010, methodology): “Scott-Blair used the fractional calculus approach to model the observations made by [Nutting (1921); (1943); (1946)] that the stress relaxation phenomenon could be described by fractional powers of time.”
The -Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey (2010, background): “[1], [21], [42], [40], so that it could be referred as the Queen function of fractional calculus(4).”
A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials (2016, methodology): “…fractional differential equations, methods of their solution and applications can be found in the books by Diethelm (2010), Hilfer et al. (2000), Mainardi (2010) and Podlubny (1999), and excellent review papers have been presented by Metzler and Klafter (2000) and Rossikhin and Shitikova (2010).”
Classes of operators in fractional calculus: A case study (2021, unknown): “PR a D β,ρ α,ωf (x) = ∞ ∑ n=0 Γ(−ρ + n)ωn Γ(−ρ)n! RL a Inα−βf (x), Re(α) > 0,Re(β) ≥ 0, (8) 9146”