On definition of solution of initial value problem for fractional differential equation of variable order

Abstract

We propose a new definition of continuous approximate solution to initial value problem for differential equations involving variable order Caputo fractional derivative based on the classical definition of solution of integer order (or constant fractional order) differential equation. Some examples are presented to illustrate these theoretical results.

Keywords

• variable order caputo fractional derivative
• variable order fractional integral
• fractional differential equations
• initial value problem
• approximate solution