Fractional calculus: A survey of useful formulas

By Duarte Valério, Juan Trujillo, M. Rivero, J. Machado, Dumitru Băleanu. The European Physical Journal Special Topics, 2013

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Elasticity for economic processes with memory: Fractional differential calculus approach (2016, background): “Theory of derivatives and integrals of non-integer (fractional) orders [1, 2, 3, 4] has a long history [5, 6].”
Leibniz rule and fractional derivatives of power functions (2016, background): “Theory of fractional derivatives of noninteger orders [1–4], which has a long history [5,6], has wide applications in physics and mechanics, since it allows us to describe systems, media, and fields that are characterized by power-law nonlocality and memory of power-law type.”
Economic interpretation of fractional derivatives (2017, methodology): “The theory of derivatives of non-integer orders [1, 2, 3, 4, 5] has been formulated by famous mathematicians such as Riemann, Liouville, Sonine, Letnikov, Grünwald, Marchaud, Weyl, Riesz, Caputo and others.”
Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation (2014, background): “The subject is nowadays very active due to its many applications, not only in mathematics, but also in physics and engineering, and has proven to better describe certain complex phenomena in nature (see for instance [2–9]).”