import matplotlib.pyplot as plt
import numpy as np

def generic_exponential(x, A, B, Gamma, beta):
    return A*(1-np.exp(-(Gamma*x)**beta))+B

x = np.logspace(-2, 2, num=200)

y1 = generic_exponential(x, 1, 0, 1, 1)
plt.semilogx(x, y1, 'b-', label=r'$\beta=1$')
y2 = generic_exponential(x, 1, 0, 1, 0.5)
plt.semilogx(x, y2, 'r-', label=r'$\beta=0.5$')
y3 = generic_exponential(x, 1, 0, 1, 2)
plt.semilogx(x, y3, 'k-', label=r'$\beta=2$')
plt.xlabel(r'$\Delta t$')
plt.ylabel(r'$D(\Delta t)$')
plt.legend()
plt.show()