A novel numerical technique used in the solution of ordinary differential equations with a mixture of integer and fractional derivatives
Provides numerical methods for solving mixed-order fractional differential equations, which are relevant for researchers in applied mathematics and engineering modeling such systems.
This paper develops numerical algorithms for solving ordinary differential equations that combine integer-order and fractional-order derivatives (Riemann-Liouville and Caputo). It proposes four discrete forms for the Caputo derivative and three numerical techniques, and shows how to incorporate classical initial conditions for Riemann-Liouville derivatives.
Using both fractional derivatives, defined in the Riemann-Liouville and Caputo senses, and classical derivatives of the integer order we examine different numerical approaches to ordinary differential equations. Generally we formulate some algorithms where four discrete forms of the Caputo derivative and three different numerical techniques of solving ordinary differential equations are proposed. We then illustrate how to introduce classical initial conditions into equations where the Riemann-Liouville derivative is included.