  A generalized fractional derivative (GFD) definition is proposed in this
work. For a differentiable function that can be expanded by Taylor series, we
show that D^Elafa*D^Beta f(t)=D^(Elafa+Beta)f(t). GFD is applied for some
functions in which we investigate that GFD coincides with Caputo and
Riemann-Liouville fractional derivatives' results. The solutions of Riccati
fractional differential equation are simply obtained via GFD. A comparison with
other definitions is also discussed. The results show that the proposed
definition in this work gives better accuracy than the commonly known
conformable derivative definition. Therefore, GFD has some advantages in
comparison with other definitions in which a new path is provided for simple
analytical solutions of many problems in the context of fractional calculus.
