The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative

In the finance market, it is well known that price change of underlying fractal transmission system can be modeled with Black-Scholes equation. This article deals finding approximate analytic solutions for time-fractional equation fractional integral boundary condition a European option pricing problem in Katugampola derivative sense. It generalizes both Riemann–Liouville and Hadamard derivative. The technique used to find generalized Laplace homotopy perturbation method, combination transform method. solution form Mittag-Leffler function. shows method one most effective methods construct differential equations. Finally, are also shown.