Fractional Diffusion Models of Option Prices in Markets With Jumps

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Logistic map with memory from economic model (2017, background): “We should note that the fractional calculus and fractional differential equations have a wide application to describe different economic and financial processes with memory and nonlocality [56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 15, 16, 17, 18, 19] in the continuous time approach.”
Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method (2013, methodology): “Cartea and del-Castillo-Negrete [11] gave several fractional diffusion models of option prices in markets with jumps and priced barrier option using fractional partial differential equation.”
New theories and applications of tempered fractional differential equations (2021, background): “Cartea and del-Castillo-Negrete developed the tempered fractional diffusion equation that governs the probability densities of the tempered Lévy flight [13].”