Fractional Calculus, Langevin Equation and Quaternions

Explore the mathematical connections between fractional calculus and the Langevin equation in this 27-minute Wolfram presentation that demonstrates how the Langevin equation can be interpreted as a half-order fractional differential equation. Learn the solution methods for this fundamental stochastic differential equation used in physics and engineering, then delve into advanced computational techniques for solving quaternion and biquaternion differential equations. Discover how these mathematical frameworks intersect and their applications in modeling complex systems, with practical demonstrations of calculation methods for these specialized differential equation types.