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In this study, we first present a time-fractional L    e ^    vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L    e ^    vy-time fractional diffusion equation of European-style options. Further, we introduce a more general model based on the L    e ^    vy-time fractional diffusion equation and review some recent findings associated with risk-neutral free European option pricing.

Fractional Partial Differential Equations Associated with Lêvy Stable Process