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.
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