A new approach to fractional differential equations

Abstract

In this work, we define fractional derivative of order ? > 0, with no restrictions on the domain of the function, and give its geometry. We derive some rules and properties for the proposed new approach and show that if fractional order converges to an integer order, then each rule converges to the corresponding rule of derivative under this integer. On applications side we show that it has ability to convert various type of FDE to ODE and vice versa. Finally, we solve several FDE given in literature through the new approach.